The thing that Americans might miss about this is that Trad Jazz, as an amateur/semi-amateur activity in the UK, was quite an active scene in pub sessions in the UK for quite a long time after the music had stopped featuring in the record charts. Generally before folk sessions really came along. The two operated in parallel, often in the same pubs, often with the same kind of people, players or punters. And distinct from the Jazz scene as such, which tended to look down on all this.

Dire Straits' "Sultans of Swing" is about this type of thing (though of course not an example of it - though the mood is right):

And a crowd of young boys they're fooling around in the corner,
Drunk and dressed in their best brown baggies and their platform soles.
They don't give a damn about any trumpet playing band.
It ain't what they call rock and roll -
And the Sultans played Creole

(Here's Dire Straits playing it live, but it takes some time to load.)

My impression is there's not too much of that around now. Pity. No, not part of "the Folk Scene" - but Folk Music alright.