It's tempting, however fanciful, to imagine that the space Scott was staring into was also something to do with the future of jazz, and his own place in it. A terrific tenor saxophonist in his prime, whose Jazz Couriers group with Tubby Hayes (who died in 1973) was the highpoint of British bop in the late Fifties, Scott nevertheless suffered from insecurity about the value of his playing, often refusing offers to sit in with the American stars he had booked to play at his club, who admired him unreservedly. Even the tetchy Charles Mingus gave praise: "Of all the white boys, Ronnie Scott gets closer to the negro blues feeling," he said in 1961. This, of course, was part of the problem. Jazz musicians of Scott's generation dedicated themselves to an idiom whose cultural roots lay largely in another continent and another racial identity, and they tended to measure their own art accordingly, becoming hypersensitive about their imagined shortcomings.
Although there has been a vital European jazz tradition since the 1920s and Django Reinhardt, it's only comparatively recently that it has seemed to offer British musicians a credible alternative to aspire to. At present, European jazz has never been stronger, with British artists the strongest of all if we accept the measurement offered by the annual Danish Jazzpar Prize (a cash reward of $34,000, and an overall budget of $250,000 for performances, broadcasts and recordings). This year's winner is Django Bates from Beckenham, the pianist, composer and bandleader (of Loose Tubes and Delightful Precipice). Three years ago, the winner was Canterbury's Tony Coe, the saxophonist and clarinettist, and these two represent the only non-Americans to have won the award - the nearest jazz gets to a Nobel - since it was established eight years ago. Significantly, both Bates and Coe abjure the bop tradition in favour of an eclecticism that draws from earlier and later forms of jazz, as well as from classical and folk music. For young British jazz musicians today, the range of influences has never been broader, though what for Scott would have been the great tradition - the lineage of bop from Charlie Parker to the Marsalis brothers - can be a burden as much as an inspiration.
For the saxophonist Julian Arguelles - whose Scapes album of last year was one of the most striking, and strikingly different, of all British jazz albums - the bop tradition is a perplexing inheritance. "I don't know how I deal with it," he says. "I go through phases. Sometimes I feel really happy playing saxophone and then sometimes I find it quite frustrating or even depressing, especially because there is a real tradition with the sax, a tradition I came up through, of John Coltrane and Sonny Rollins. It really is hard to not sound like that; it's in the nature of the instrument to sound very, well, jazzy. I listen to Coltrane and Rollins and just think that that's what the instrument does best."
Arguelles finds alternative models in classical and folk music, but recognises the importance of a European jazz tradition too, citing the examples of the Norwegian Jan ("Officium") Garbarek, the British John Surman and the Brazilians Hermeto Pascoal and Egberto Gismonti.
At 23, the pianist Nikki Yeoh is perhaps the most exciting British jazz musician of her generation. Yet to make a record, she came to prominence after sitting in on a jam session at the Jazz Cafe as an amateur, where she impressed Courtney Pine sufficiently for him to pick her for his band there and then. She has since toured with Neneh Cherry, formed her own trio, Infinitum, begun a series of solo performances and written for the contemporary classical keyboard sextet Piano Circus, who programmed her piece alongside works by John Cage. "I don't see myself as fitting in with either the European or American traditions", she says. "There isn't so much pressure these days to fit in with any category. People are starting to get their influences from all sorts of different places."
Yeoh does, however, recognise national differences in the way jazz is passed on from one generation to the next. "In the US, there's a tradition of bandleaders as teachers. With someone like Dizzy Gillespie, or Wynton Marsalis now, they wouldn't just get you out of bed and say, `Right, G flat minor, ninth chord!' They'd explain how it works, and pass their knowledge on to members of the band. That sort of thing isn't woven into the fabric of the cloth here."
Yeoh is currently working on a commission for this year's Bath Festival which involves harmonising the sound of the spoken word from readings in different languages of one of her own poems, for a composition for 14 musicians and a video projection.
Video projections? Compositions for six pianos? John Cage? You can almost see Ronnie Scott shaking his head with disdain and reaching for the packet of fags. He would, however, surely love Yeoh's improvisation on Coltrane's "Giant Steps", and thrill to Arguelles' tender reading of "Too Young to Go Steady", the corny standard Coltrane transfigured into rare art. Staring into such a space, perhaps the future of British jazz wouldn't look too glum, even to Ronnie?
Julian Arguelles Quartet 8pm today, Julian / Steve Arguelles Duo 3pm tomorrow, at Blackheath Concert Halls, 23 Lee Rd, London SE3 (0181-463 0100)