A few miles from where I live once a month there is an "English Session" - in a pub called "The Welsh Harp", which I think is a nice touch. (Near the Abbey Church in Waltham Abbey, on the first Wednesday of the month.) It's thebonly "English Session" in the district within the known universe (it's a universe which stretches about 15 miles around Harlow.).

One of the main regulars plays a sort of giant Lithuanian Zither. There's normally a bodhran there and a guitar or so, as well as fiddles, whistles and squeezeboxes. Most of the people you see are people you'd be likely to run into at any other sessions.

What qualifies it to be called English is that the tunes tend to be from that sort of tradition. Unless people feel like playing one from Scotland or Ireland or Lithuania.

So I don't think anyone need worry about it being exclusive or purist. Which is the most English thing about it, maybe. The good-natured sort of English that is, not New English. Not Brit, thank God. (Almost Irish in fact - but a bit more solemn in its frivolity.)