To have a go at answering the original question: it varies depending on where you are, and which session you're playing in.

For instance, there's quite a strong Irish scene in certain parts of England, especially where there has historically been a lot of Irish immigration in the last century. London, Liverpool and Manchester spring to mind.

Around where I have lived in the past ten years (East Anglia, N Yorks and Bucks) I've been playing in sessions where it is predominantly English styles of music which are played (but then I have been hanging round with a bunch of morris dancers). But as has already been pointed out, over the past few hundred years, there has been a lot of cross fertilisation between styles found in the UK and Ireland. "Woodland Flowers", made so famous by Dartmoor melodeon player Bob Cann, is one of Jimmy Shand's tunes, I'm told!

There are musical styles which are considered characteristically English (not exclusively so), but there's a lot of regional variation. So yes, it is possible to walk into a session, listen to a few tunes, and have a fair guess at whether or not the tunes are mainly English in style.

Fair comment?

Jane