It seems only yesterday that Mayor Fiorello H. La Guardia, cleaning up Times Square, ran burlesque out of 42d Street, clear to Union City, N.J. Actually that happened more than 40 years ago. It is something of a commentary too that Ann Corio, once a supreme practitioner of the torrid striptease art, has brought her stage memoir, ''This Was Burlesque,'' back to Times Square, to the Princess Theater, and it has an almost uplifting effect on the neighborhood.
''This Was Burlesque'' has been around since 1964, when, with Miss Corio as star, director and author, it opened on Second Avenue. It later moved to Broadway, where burlesque was already a matter of distant recall, and then went touring. Now back on Broadway, the show appears less than titillating as it lets everything hang out in the flesh in the time-honored melange of girls and gags that really was burlesque. The jokes and double entendres are old, the way the show is done is old, even many, but by no means all, of the people who laughed loudest in the preview audience betrayed an age that hinted their visit was a pilgrimage to the past. Miss Corio, who looks radiant, does it all by the book and, whether you like the book or not, it is to her credit that she catches the flavor of the old burlesque with little attempt to ennoble or elevate it. This is close to the real thing.
There are strippers, ''exotic dancers'' in more suave terms, who peel down to all but the final essentials. Two of them, Tami Roche and Lili Chanel, are women, extremely eye-catching and generously endowed, and one, an innovation to the take-it-off circuit, is ''Patrick,'' a male stripper whose mission is to arouse and amuse the ladies in the house.
Burlesque comics were something special and there is no dearth of them here. Phil Ford and Jerry Kurland do song-and-dance comedy that is one of the high points of the entertainment. Claude Mathis, who will be 81 years old soon, runs through jokes and routines older than he is, but he does them, baggy pants and all, in the revered traditions of the trade, which at times is a lot of fun. Dexter Maitland, Charley Naples (he does tricks and comedy in the guise of Chaplin), Frank Vohs, plus the nine ''Burley Cuties,'' contribute to the particular flavor of nostalgia that permeates the house. Miss Corio, of course, puts it all into focus.