The room where Allen plays is jammed full of tables covered with cheap tablecloths. The ceiling is low with a covering of stained polystyrene tiles and the lighting would look sub-standard in a motorway cafe. Patrons take their tables with a look of wonderment which is only partly explained by the imminent presence of one of the most recognisable faces in cinema.
Almost everybody paying the $35 minimum charge speaks French or German or a Scandinavian language. Michael's is a genuine tourist trap where the visitor can experience a side of New York life not usually explored in Allen's sophisticated movies.
"This is a shrine," says John Forsyth, the manager of Michael's. "This is the place where Woody Allen plays." For much of the next month, however, the shrine will have to sell its over-cooked sirloins without Woody's help because he's heading for Europe, on a 22-day tour that takes in 14 cities and starts next Sunday in Madrid. On 18 March, at the Festival Hall, Londoners will get to sample Allen's jazz without the flavour of Michael's cooking oil - and not everyone's sure that's for the best.
"I think people in Europe should try and see Woody but I think here at Michael's you get a better atmosphere," says Christa, an advertising executive on holiday from Frankfurt. Her companion Anton agrees. "This is the real Woody Allen, that is why we have come. This is New York."
Around nine o'clock anticipation begins to build. Barbara Dreywitz brings her tuba on stage and her husband Dick unloads his trombone. Allen is 60, the other members of the band seem older. After the Dreywitzes comes John Booker with his trumpet, then Eddie Davis sits to tune his banjo.
"He usually slides in here invisibly like a little worm just before the show begins," one of the barmen told me earlier. I don't think he was trying to be rude. It was just his way of describing Allen's extraordinary entrance. As 200 people struggle with indigestion and heat in the crowded room a little guy in glasses pops up on stage and everybody knows his face. There is immediate silence - only sudden nudity could have grasped everyone's attention so fast - and then Allen begins to play. There is no announcement, just some reedy chords from an ancient clarinet.
Allen prefers the old-fashioned rhythms of turn-of-the-century Louisiana. His first song tonight is "In the Shade of the Old Apple Tree", a pop tune from 1905. He has told others that he became obsessed with jazz in his teens and began by playing the saxophone but found the instrument too technically difficult. He then switched to the clarinet, and heard some records by the New Orleans clarinettist George Lewis - and so began a relationship which has outlasted all his other marriages and affairs.
"I think he plays the traditional New Orleans jazz because he feels more technically suited to it," says Cynthia Sayer, who acted as musical consultant on Allen's Purple Rose of Cairo and will play piano on the European tour. "He likes bebop and straight-ahead but they are more difficult. Traditional is an ensemble style with fewer individual solos and I think that may suit his character."
The first song ends and is met with thunderous applause. Allen is dressed in brown corduroys and a white open-necked shirt. He often takes off his famous glasses to remove perspiration, and around the room people nudge each other with knowing smiles - as though without his specs they can suddenly see the real man.
Allen chooses to play a true antique. Most clarinet players use the Boehm system but Allen works with the Albert, which uses a wider bore and a virtually obsolete fingering method. His clarinet produces tremendous volume, and fills Michael's Pub with a sound that is often mournful and comic at the same time - much like Allen himself.
The band that plays at Michael's is called the New Orleans Funeral and Ragtime Orchestra but except for banjo-player Eddie Davis it will not be following Allen to Europe. Most of the band members actually prefer to play the Chicago jazz of the Twenties, though they are more than happy to indulge the star when he "drops by" Michael's every Monday. For his grand tour Allen wanted something more authentic.
"The Ragtime Orchestra has fine musicians," says Sayer. "They just don't necessarily lean towards Woody's style. The tour will get a lot of attention so I think he wanted a purer version of what they play every Monday night."
On stage the band has moved to a faster tempo for a song made famous by Sidney Bechet. As he plays, Allen seems genuinely lost in the music, at one remove from the audience, even though it includes his controversial girlfriend, Soon-Yi. Don't expect any jokes: in 25 years Allen has never been know to address the audience directly.
"We were really surprised when he decided to go on tour," says Sayer. "He tends to be very shy about his music." As tonight's show ends there's plenty of applause but Allen has clearly heard an inaudible fire alarm for he disappears like warm bagels on a Sunday morning.
"It's always been like this, for 25 years," says John Forsyth. "He has never changed his routine. He comes, he plays, he leaves." That's Woody. After all, didn't he once say 80 per cent of life is showing up?
! RFH, SE1 (0171 960 4242), 18 March.