FLORENCE; VISIT PRIVATE PALAZZI IN THIS ENCHANTED CITY

''Almost everything of importance is still there, so that to the miracle of achievement is added the miracle of survival.'' The words were written by Vincent Cronin. The object of his admiration and praise has the green waters of the River Arno flowing through its heart and the foothills of the Apennines at its back; it is the city of Florence, that close-knit medieval nest of streets and houses, squares and churches in which the early Renaissance was so astonishingly hatched - the light, measured architecture of Brunelleschi and Alberti; the serene sculpture of Ghiberti and the more emotional but balanced sculpture of the great Donatello; the delicate grace of Botticelli's paintings and the classical solemnity of Masaccio's.

They are ''still there,'' and so also are superb works of the second, more grandiose, birth of artistic heroism: the late 15th- and early 16th-century High Renaissance of Leonardo and Michelangelo and Raphael.

Florence remains the most overwhelming and enlivening experience for any traveler who not only relishes beautiful cities but loves the supreme period of Italian culture, for anyone who wants to see an incredible array of excellent paintings and sculpture and architecture at firsthand and at the same time feel something of the atmosphere lingering in the place where the enlightenment of humanism broke through and classical ideas were freshly appreciated, five centuries ago, with such energy, discovery, self-confidence, and elegance.

''You know why the hotels in Florence are filled 11 months out of 12 each year?'' a visitor was asked recently by a Florentine taxi driver. ''I tell you. It is because of half a dozen men of genius working 500 years ago!'' One can't help wondering what the sculptor of the huge marble ''David'' or the painter of the ''Primavera'' would feel about their role as tourist attractions. But the fact is that Florence is a Mecca for tourists, today as much as ever.

There is an almost continuous holiday atmosphere, and of course, any tourist (even in the winter months, as I discovered on a brief visit) is always conscious of fellow tourists. You only have to stroll across the (mercifully pedestrianized) Ponte Vecchio - the bridge, with its rows of tiny goldsmith and jewelry shops and its central, irresistibly romantic viewpoint up and down the river edged with palazzi to see more cameras than you can count. You only have to go shopping in the morning or evening along any of the streets that branch outward from the Piazza del Duomo, where the immensely decorative cathedral and baptistry and Giotto's bell tower stand, to find that not only tourists but Florentines themselves adore crowds. Indeed, it is a Florentine tradition going back at least as far as the Renaissance to spend as much time as possible out in the dark narrow streets of their city, to congregate in the open and exciting squares, and to frequent the hundreds of small shops. . . .

In the face of such melee (which provides, of course, its own kind of delight), what hope is there of an exclusive visit to Florence - something out of the ordinary run? Well, one such special tour is newly offered for 1983. It promises to open some doors that are generally shut, offering private occasions in the grand houses of noble Florentine families, people still living in the most beautiful Renaissance and baroque palazzi.

The tour is organized by the London-based Country Homes & Castles company, which specializes, as its name implies, in arranging for people to visit as ''personal guests'' in country houses in Britain, ranging from Scottish castles to humble thatched cottages. Country Homes & Castles has been going strong since 1965. Susie Worthy, who has been running it for the last three years with considerable charm and aplomb, is now extending her territory to include French chateaux and Florentine palazzi.

The Florence tour takes place twice in 1983: April 10-20 and Oct. 2-12. It kicks off unpredictably enough (after a welcome dinner in London at a private residence) with a full-day tour to Gloucestershire, exploring the rollicking countryside in that part of the Cotswolds that has earned the epithet ''royal'' since certain young members of the royal family came to live there.

But the main purpose of this day is to have lunch with a Maltese baron and his wife in their 18th-century Palladian-style house. The Baroncino de Piro's lineage winds backward anciently enough; his family has apparently been connected with the Knights of Malta since the 1350s. He speaks impeccable English, and has an affable sense of humor. He also knows and loves Florence. He will accompany the tour when it departs the next day from a London airport to Florence (via Pisa), and he is certain to add to the whole trip the flavor of his own knowledge of the city and its surroundings.

Strictly limited to a maximum of 30 people, the group will also be shepherded by an English guide who lives in Florence. Her name (she is married to an Italian) is also one to reckon with: Antonia Lanza d'Ajeta Macartney Filgate.

The six full days actually spent in Italy are a neat balancing act between the expected and the unexpected. The more expected includes the ''David'' and other supreme sculptures by Michelangelo in the Accademia delle Belle Arti and in the Medici chapels. You will see the Ghiberti ''Gates of Paradise'' with (so far) just one of the tan bronze panels radiantly cleaned. You will see the cathedral, of course. The Uffizi Gallery's unrivaled collection of paintings is scheduled, and so is the last residence of the Medici family, the Pitti Palace, intimidatingly grand outside, a large friendly gallery of Renaissance art inside. (As a side glance here, look out for the delightful little 18th-century bathroom.)

One of the special experiences will be a visit to the Palazzo Davanzati, a late-medieval palazzo that fell on bad times, was refurbished in the Renaissance , and today has been most attractively restored as a Museum of the Florentine home in the early Renaissance.

Several trips outside Florence are included. One will take the group to see the gardens of two Medici country villas. Another is to Siena, with its medieval city walls and gates and its black-and-white-striped marble cathedral, an impressive example of Italian Gothic. Lunch that day will be at a lovely country hotel, Locanda dell' Amorosa, which boasts both fame, among Italian gourmets, and freedom from ''the heavy tread of the modern tourist.'' San Gimignano, the famous Tuscan medieval town will be yours for a morning - its cobbled streets, ancient walls, 13 towers (out of an original 72), and fine views over the countryside - yours, though doubtless shared with many other tourists. (The choice of April and October, however, seems calculated to avoid the worst crush of sightseers, and also, presumably, the most stifling heat.)

At Certosa you will see the slightly disturbing frescoes of the mannerist Pontormo, and at Arezzo the wonderful and elevatedly ordered frescoes of Piero della Francesca. Finally, time is allowed before flying back to London for a peek at the Leaning Tower, piazza, cathedral, and baptistry at Pisa.

Dispersed merrily throughout these items are the visits to noble Florentine families (of which more later) and a number of times to yourself. Though the relaxed pace of Italian life may tempt you to take a siesta or two back in your room at the luxurious Grand Hotel Baglioni - resist! ''Afternoons free'' and ''evenings at leisure'' do not only mean that you can shop for leather goods or will have to find your own place to eat (if I have a criticism, it is that there are rather too many occasions when meals are not specified on the itinerary), they also mean that now is the time to see some of the wonderful things in the city which the official program simply couldn't cover. You will inevitably be on foot, but much is within easy walking distance. Advice will certainly be plenteous.

The Baroncino de Piro will almost certainly enthuse about the science museum. ''I'd almost say go there rather than the Uffizi,'' he exaggerates. ''It ends where the science museum in London begins - marvelous.'' And he will wax lyrical about an astoundingly interesting shop, the Farmacia Santa Maria Novella, fine for unusual gifts, even an after shave called ''Contro il fuoco del rasoio'' (ask him to translate).

Susie Worthy might possibly persuade you to trace the private covered corridor that links the Uffizi with the Pitti via the Ponte Vecchio, with a stopping place en route so that the Medicis could hear mass from a screened balcony in the church of Santa Felicita.

I would strongly recommend an early morning (beat the crowds) climb (it can be partly achieved by taxi) up to the peace and sanctity of the spacious but intimate Romanesque church, San Miniato al Monte. Wait until you are at the top of the flight of wide steps leading to the church (Dante was here before you, by the way), keeping your gaze fixed on the striking facade of white and dark-green marble, and then turn round suddenly. The wide-stretched view of Florence you then see in the morning light will quite simply defy praise - an unforgettable gasp of beauty, the multiplicity of orange-red roofs set out below, the impressive length of still-standing city wall to your left, the deep cypresses, the Arno, the notable spires and palazzi, Brunelleschi's unique dome holding sentinel like the head of a rather pious giant over it all, and beyond, the magnificent shape of the long hills. To go to Florence and miss this would be a crime. And then there is San Miniato al Monte itself, a church of intangible qualities, age, and grace.

Then everyone will point out that you cannot possibly go without a stroll through that most loved of Florence piazzas, where ceremonials are still performed and where Savonarola met his cruel martyrdom. Here is the Loggia dei Lanzi, sheltering marvelous statues, the gentle splashing sound of the Neptune fountain, the towering Palazzo Vecchio . . . and yet it is somehow a square that doesn't intimidate, the Piazza Signoria. Nor can you miss seeing the sculpture collection in the Bargello, or the Masaccio frescoes in the Carmine; or leave without delighting in the energetically skipping arches of Brunelleschi's arcade of the Piazza Santissima Annunziata, or giving at least a glance at the magnificent Boboli Gardens.

Maybe you will have time on this very full tour for some of these things; maybe they will have to wait until your next visit. It is that kind of city - no sooner are you on the road away from it than you are plotting the how and when of your return.

But you will take away with you something that most visitors never experience. Perhaps it will be worthwhile forgoing the interior of Santa Croce and even the unworldly and innocent frescoes of Fra Angelico in the San Marco Museum. Ultimately, it is a matter of taste and opportunity. But it is certainly fascinating that there are noble families still living in some of the finest palazzi in Florence: the Palazzo Rucellai, the Palazzo Gondi, the Palazzo Capponi, the Palazzo Guicciardini among them.

Tact and a respectful secrecy are involved in arranging for private lunches, receptions, and even a farewell dinner at such places. But Country Homes & Castles promises - without naming names - several such visits, and they are likely to be more than memorable. One item on the agenda, for instance, reads: ''Lunch as guests of a leading member of the Florentine nobility at her sumptuous palazzo'' followed by a visit ''to her other palazzo,'' housing an outstanding private art collection. This mainly consists of 17th-century Florentine paintings, with one or two gems of Renaissance painting here and there.

The wait-and-see element of this tour only adds to its spice. Certainly it will include glimpses of traditional living on a grand scale - not only the splendors of Renaissance Florence itself, but the hospitality of some of the proud people living in it.Practical information: For more information on this tour to Florence (and tours in Britain) write Susie Worthy, ''Country Homes & Castles,'' 138 A Piccadilly, London W1V 9FH, telephone 01-491-2584. Cost per person $2,475 (plus $248 single supplement), plus special group flight New York to London to New York, $627.