New York

If ever one needed an excuse to explore the cramped and historic precincts of Lower Manhattan, this is the year. For one thing, 1983 is the centenary of the Brooklyn Bridge, the legendary silver span that connects the bottom of Manhattan with the grand duchy of Brooklyn. Frequent events commencing with the May 24 birthday are bound to bring fresh droves of visitors downtown the rest of the year.

Also, the British are celebrating the 200th anniversary of their official departure from old New York, which in 1783 barely extended above the narrow lower wedge of the island. A giant free-form festival (see ''practical details'' at the end of this article) will run well into June and beyond with a certain emphasis on the British period.

Never needing a prod to visit the narrow streets of the world below Chambers Street, I hopped a subway on a blowy spring day and, emerging near City Hall, whiffed the familiar air of Lower Manhattan. The smell is both real and imagined: power, money, history, fish. Mayor Ed Koch was, for a change, not visible about City Hall, but Brooklyn District Attorney Elizabeth Holtzman stood on the steps of the dignified Louis XVI-style building - where there always seems to be a crowd - telling reporters and passersby she was launching a campaign to bar discrimination by lawyers in the selection of jury members.

Just southwest of the greening City Hall Park - where the British hanged Nathan Hale for spying on them in the costume of a schoolmaster - stands a splendid but somewhat overlooked skyscraper, the Woolworth Building. This wonderful 1911 Gothic pile was the tallest peak in town until the Empire State and Chrysler Buildings arrived uptown around 1930. I was glad to see that the longstanding scaffold and wood frame had been removed; the restored terra cotta and limestone looked fresh and new. At the rear of the gilded, mosquelike lobby is a tribute to Frank W. Woolworth, who built this ''Cathedral of Commerce'' without mortgage financing - ''unique in the history of modern construction.''

One block south at Broadway and Vesey, a patch of sky opened up and there stood steepled St. Paul's Chapel, framed in the near distance by the shining towers of the World Trade Center: then and now in one shot. Music drifted from New York's oldest church; inside I found the Columbus Trio warming up before an audience of three for a Brahms recital they would give an hour later as part of a daily lunchtime program. Along a pink wall I paid respects to the pew George Washington used when New York was briefly the nation's capital.

At Broadway and Wall Street I peeked into another of Lower Manhattan's favorite noonday refuges, Trinity Church, which has a musical program of its own. Britain has left the church some fond mementoes. Three of the original bells were a gift from London in 1797, and on a wall at the west side of the 21/ 2-acre churchyard hangs a little plaster cherub. It survived the bombing of a London church destroyed by the Luftwaffe in 1941 and was presented to Trinity Church in 1964.

Now I headed east on Wall Street into the darkening maze of closely clustered financial buildings. At Wall and Broad stands the smudged, century-old Federal Hall National Monument with a statue of Washington on the steps, the very spot where he took the oath of office. Inside there are various colonial exhibits and a singer named Linda Russell in flowing period dress who does colonial folk songs and ballads on request. She was busy on the phone, so I walked down Broad Street to catch a show I knew was on.

At the New York Stock Exchange I took the elevator to the third floor and crossed the red-carpeted Visitors Center to a catwalk above the Trading Floor. Through a glass panel we vicarious investors watched the chaotic noonday ritual, men in dark suits and blue smocks rushing about like commuters trying to catch a departing train. The wood floor was hopelessly littered with paper - not, however, ticker tape, which has long since been replaced by flashing green figures on mounted TV screens.

Several blocks south, I came out of the financial cavern and into the bright, open, babbling atmosphere of Battery Park. A dozen different languages seemed to be asking the same question: ''Where do you get the ferry to the Statue of Liberty?'' Both the statue and Ellis Island were visible across the water, which may lack the color and din of Hong Kong harbor but always has a red tug or orange Staten Island ferry to brighten the blue-gray canvas.

Mother Liberty is due for an ambitious remodeling, but the old gentleman in the booth selling excursion tickets told me work wouldn't begin until 1984, ''and even then you'll be able to land out there, and the work will be more interesting than anything they got now.''

Next stop, as I headed up the west side of the Manhattan wedge, was the World Trade Center. Even more than its 107th-floor observation deck, its score of restaurants, and its myriad shops, the WTC lures me with its half-price Broadway ticket booth on the mezzanine. With musicals charging $40 and up per ticket and plays $32 to $35, one is foolhardy not to use New York's budget TKTS posts. As the relaxed clerk at the nigh-empty booth told me, ''We open at 11 in the morning, four hours earlier than they do at Times Square, so you get a better selection down here, and there's almost never a wait.''

With the arrival of the 23-story Vista International next door, Lower Manhattan has its first hotel in 150 years. Weekdays the Vista tends to be full of business travelers and is not a particular bargain anyway, but there are weekend packages for as low as $79 a night for two. The price includes guided walking tours of the area and a minibus excursion across the tip of the island to the Brooklyn Bridge, which will hold sound and light shows this summer. Yes, son et lumiere on the East River.

If that's not enough, the first phase of the South Street Seaport - New York's answer to Boston's Quincy Market - will be finished later in the summer, bringing back some of the dockside flavor of 200 years ago to the area south of the bridge. Just one more excuse for making the downtown trek in 1983.

Practical details

Though many of the events scheduled for Britain's Salute to New York will come and go with the spring flowers, the following are among those that will last well into the year:

Until June 15: Works by Constable, Gainsborough, Reynolds, and Turner, the National Academy of Design.

Until June 18: Exhibit of English table settings, Tiffany & Co.

Until July 3: An exhibition of paintings by Winston Churchill, the National Academy of Design.

Until July 30: Portrait drawings by Hans Holbein of the court of Henry VII, the Pierpont Morgan Library.

May 14-Sept. 25: 60 years of sculptures, drawings, and lithographs by Henry Moore, Metropolitan Museum of Art.

May 24-Oct. 2: Achievements of important Anglo-Jewish artists of the 20th century in Britain, Jewish Museum.

Until Sept. 4: Major exhibition of the paintings of John Constable, Metropolitan Museum of Art.

Until Nov. 27: Display of British New York, 1664-1783, at the Museum of the City of New York.