It's actually quite difficult to miss the folk scene in Sheffield. there's loads of it! Sheffield Uni has a folk society with about 300 members that have ceilidhs every couple of weeks and a Wednesday night session at the Red Deer on Mappin St. http://www.ceilidhsoc.org/
There are Sunday night sessions with a good mixture of students and local musicians at the Kelham Island Tavern on the 1st and 3rd Sunday of the month.
I'm sure Jim will be on to tell you about other stuff including the Sheffield Folk festival that is happening at the end of the month.

Cheers
Rich
www.cruciblemusic.co.uk