Transatlantic salute; Britain is bustin' out all over -- in New York

Since mid-April Britain has been saluting New York with an array of events and entertainments in the fields of commerce and the arts. Indeed, this expansive transatlantic gesture has been a salute in the form of an embrace.

The theater, as well as dance and music, has played its important role in the festivities. Official representation has been assigned to such troupes as the Actors Touring Company of London, the Brighton Theatre Company, the Fool's Theatre Company of Oxford (premiering a new play), the Joint Stock Theatre Group , the Hesitate And Demonstrate Company, and the Moving Picture Mime Show.

By coincidence (and not part of the official salute), the Royal Shakespeare Company brought its exhilarating ''All's Well That Ends Well'' to Broadway. Originally planned for a limited 16-week run, the critically acclaimed revival closed after only six weeks due to insufficient public response.

The Actors Touring Company came to New York with a repertory of two plays, Sir John Vanbrugh's 17th-century comedy ''The Provoked Wife,'' and ''Quixote,'' an adaptation of Cervantes.

In its version of a seldom-produced Restoration work, the company makes a virtue of economical staging and vigorously stylized performance. The typical plot concerns a drink-sodden misogynist of a husband, the wife who is tempted to betray him, her would-be lover, and her niece, who wins the heart of a reluctant bachelor.

The pattern of verbal encounters and intricate plot maneuvers is admirably pursued by this attractive company. Except for a clownishly caricatured Lady Fancyfull, the performance offers a diverting backward glance at 18th-century comic intrigues. One of director John Retallack's more amusing interpolations involved a violin-and-tuba duet. Though the scenery consists of but four frequently rearranged benches, the costumes match the flourish of the entertainment.

A show of quite another kind is taking place in the Astor Gallery of the New York Public Library at Lincoln Center. It is called ''At Home Abroad: Anglo-American Stage Stars, 1783-1933,'' and runs through July 9. In their elegant salute, William Appleton and Mrs. Babette Craven have assembled a rich and glamorous overview. With playbills, portraits, scene pictures, and ceramic figures, the exhibition documents the course of a long and fruitful stage relationship.

A catalog summary says the exhibition focuses on two significant theatrical periods development and two important groups of performers. Among the stars of the first group are George Frederick Cooke (''the first great English actor to visit the United States''), the Keans (Edmund and Charles), Macready, Forrest, the Booths, Fanny Kemble, Joseph Jefferson (whose grandson made a career of ''Rip Van Winkle''), and the Wallacks. The exhibition also pays tribute to Ira Aldridge, ''the first internationally famous black actor,'' who reversed the trend of the times by emigrating from the US to England.

The second part of ''At Home Abroad'' centers on musical-stage performers between 1840 and 1933, when ''New York began to amortize its debt to London.'' The counterinvasion included minstrel shows as well as musicals such as ''Ixion, '' starring Lydia Thompson, and ''The Belle of New York,'' starring Edna May. Beginning in 1920, ''not only did a flood of American performers successfully appear in London, but many of them settled there permanently.'' Among the stars of the 20th century who were at home abroad on both sides of the Atlantic were the Astaires, Dorothy Dickson, Lew Leslie's ''Blackbirds,'' Noel Coward, Beatrice Lillie, Gertrude Lawrence, and Jack Buchanan - all of whom figure in the exhibition.

While the theatrical manifestations of ''Britain Salutes New York'' provide a particular focus, the continuing Anglo-American stage relationship has manifested itself in other ways this season. ''Cats'' may not be quite ''now and forever,'' but it's still drawing capacity audiences to the Winter Garden Theatre for its back-alley musical celebration of feline rites and rituals. This has been the only big new musical hit of the season.

British plays (sometimes with American casts) have included C.P. Taylor's ''Good,'' David Hare's ''Plenty,'' James Roos-Evans's ''84 Charing Cross Road'' (from the Helene Hanff book), Simon Gray's ''Quartermaine's Terms,'' Noel Coward's ''Private Lives,'' Caryl Churchill's ''Top Girls,'' and Peter Nichols's ''Passion.''

''Top Girls'' illustrates a novel example of Anglo-American theatrical exchange. Miss Churchill's brilliant treatment of women's emergence from male dominance opened in December with its original London Royal Court Theatre cast. When the time came for the British actresses to return home, they were replaced by a top-flight American company, which has kept the play successfully running at the Public/Newman Theatre.

Meanwhile, as his contribution to the recently formed exchange program, producer-director Joseph Papp has been readying Thomas Babe's ''Buried Inside Extra.'' When the play about a metropolitan newspaper concludes its Public Theatre run, Dixie Carter, William Converse-Roberts, Sandy Dennis, Vincent Gardenia, and Hal Holbrook will travel to London to perform the work at the Royal Court Theatre.

The stimulating exchange is timely in this year of ''Britain Salutes New York.'' It is a long-term salute with far-reaching artistic possibilities.