Acker Bilk, Kenny Ball, The Temperance Seven, The Alberts and many others achieved fame outside Jazz circles in the period. There were many regional bands such as The Jazz Messengers (Scotland).
The revival seemed to peak about 1964 and fade out by about 1965/6.
That's when the The Bonzos came on the scene, sending up the Trad Jazz scene until the Bob Kerr split, when they switched to a Pop/Rock style.
In the Seventies the likes of Acker Bilk and Kenny Ball got occasional musical spots on chat shows like Pebble Mill At One.
I assume there are plenty of venues in big cities and there seem to be a few pubs and clubs around offering occasional gigs. (For instance, Bill Posters Will Be.) At least half a dozen Cambridge pubs have regular jazz, though it's mainly modern jazz by small, informal combos.
However there is no major outlet, not even on cable TV. Mainstream record shops rarely have a significant stock of Trad Jazz (plenty of modern). At least there are the excellent speciality shops such as Garon Records (King St., Cambridge).
As a further example, in 1999 there was in-depth coverage of the Edinburgh Festivals on BBC2 and Channel 4, covering components such as the Tattoo, the Fringe (comedy), the Book Festival and the Film Festival but there was no coverage of the Jazz & Blues Festival (or the Folk Festival).