The Burrell Museum. Glasgow's new edifice houses an outstanding art collection

One day in the late 1920s or '30s a lean, upright Scotsman of fairly advanced years visited Glasgow's imposing city art gallery, at Kelvingrove. He had come to look at a particular group of paintings, donated to the museum in 1925 by one man. He discussed them with an attendant. ''Oh,'' said the man, ''I don't know much about them. We've got to keep them together, that's the condition, but we'll likely scatter them when the old buffer dies.''

What the unsuspecting official hadn't quite appreciated was that the unassuming visitor was, in fact, the ''old buffer'' himself - William (late Sir William) Burrell, a very wealthy ship-owner and art collector quite extraordinary.

Fortunately, the attendant was wrong in his prophecy of Glasgow's eventual treatment of Burrell's treasures.

The city was later to become the recipient of his entire collection (also to be kept intact), consisting of about 8,000 items, spanning some 4,000 years of cultural history, collected over a period of 80 years. Now, in 1983, this vast act of generosity has been accorded the recognition it deserves. It is at last housed in a superb modern building, specially designed, in a lovely park, and only about three miles from the center of Glasgow.

''At last'' is a fair comment. When the Queen officially opens the Burrell Museum to the public on Oct. 21, it will be just two months under 40 years since he decided to give his collection to the city of his birth. Most of it has been in storage, unseen, for that time. A few special exhibitions of selected items have been held - stained glass, tapestries - and a number of his finest paintings have been on view at Kelvingrove. But the magnificent range of Burrell's collection has simply been unavailable for the public to see until now.

An astonishing string of delays and difficulties intervened. Not the least of these was Burrell's admirable insistence that the gallery should be out of range of the industrial city's polluted air, and in a rural setting. Several proposed sites failed to materialize. The final choice of south-side Pollok Park was made possible by its donation to the city by the Maxwell family, and by the fact that Glasgow had now become a ''smokeless'' zone. The park is as ''rural'' as could possibly be imagined inside a city: out of sight of housing and even graced with Highland cattle.

Ever-rising costs, the necessary priority of Glasgow's housing shortages, and the difficulty in obtaining essential government grants were further problems in the way of realizing a building which, in the event, has cost a staggering (STR) 20.6 million (about $30 million). It is understandable that Burrell's generosity might at times have seemed to the Glasgow Corporation more of a millstone than a blessing.

But all that is history now, and the inhabitants of Scotland's second city, who are in the throes of image-changing from industrial wasteland to tourist and conference center, can justifiably boast an incomparable new museum in a delightful park and woodland, displaying with taste and originality one of the world's great private collections.

Dr. Richard Marks, keeper of the Burrell Museum and a specialist in medieval art, emphasizes the collection's tremendous range and breadth - it covers, he says, ''the whole gamut.''

Burrell had less money than some of the big American collectors, but Dr. Marks mentions the Frick collection in New York as comparable, though Frick was ''more of a specialist.'' In Britain, London's Wallace Collection is similar in scale, perhaps, though quite different in its interests. More telling are the facts that, although it was brought together entirely by the one man, and most concentratedly over two decades in the '20s and '30s, Burrell's collection includes a showing of medieval stained glass that ranks with the holdings of such large institutions as the Cloisters in New York and the Victoria and Albert Museum in London. His Persian, Indian, and Caucasian rugs and carpets likewise compare with the Victoria and Albert's. His medieval tapestries are literally worth coming from the other side of the globe to see. His Chinese ceramics and bronzes (he particularly loved the bronzes) are surpassed by only three or four other United Kingdom museums.

And his collection of 19th-century French paintings, particularly the numerous Degas and Boudins, is quite exceptional. But it is in the late Gothic and early Renaissance periods in Northern Europe where Burrell's eye and preferences show to the greatest advantage.

Individual items in the collection are a delightful matter of choice, but a brief acquaintance stamps certain splendors on the memory. There is a superb small Manet; a wonderful early French Gothic boxwood carving of the Virgin and Child; a brilliant and colorful Roman mosaic fragment of a cockerel; a large and tranquil polychrome ceramic figure of a disciple of Buddha; an irresistible ceramic watchdog of the Han dynasty, of beautiful ugliness; and the tiny ''Temple Pyx'' of three sleeping soldiers in bronze gilt, one of the few but outstanding Romanesque objects: of the 12th century, either English or German.

There is also the impressive tapestry - one of the finest Franco-Burgundian tapestries anywhere from around 1450 to '75, depicting ''peasants hunting rabbits with ferrets.'' And a superb late 15th-century ''millefleurs'' tapestry - Franco-Netherlandish - of ''Charity Overcoming Envy.'' There is a glorious stained glass panel of the prophet Jeremiah, vividly red and blue, recently identified as one of the earliest surviving examples of European glass. It was commissioned around 1140 to '45 by Abbot Suger for the Abbey of St. Denis, just outside Paris.

And one can only mention briefly the silver, the armor, the misericords, the glassware, the Japanese prints, the drawings, the needlework, the furniture.

Out of some 500 pieces of furniture, the most brilliant example (still being meticulously worked on in the conservation department during my visits, in preparation for its pride of place at the grand opening) is a remarkably elaborate English walnut bureau cabinet of around 1705.

And this is a star item in a collection made by a man with an overwhelming preference for oak. ''Mark my words,'' he once said to one of the many dealers who advised and sold works to this indefatigable buyer of treasures, ''you always come back to oak.'' It is a remark that hints something of the straightforward pleasure in strong qualities of form and color (rather than line and delicate elegance), that indicates the sound judgment and discriminating eye (rather than the academic expertise) of a collector whom Kenneth Clarke once characterized as ''not simply an amasser: He was an aesthete.''