well, as an Open Studies 'attendee' at warwick , I was apalled at the lack of folk music, apart from the Arts centre(money-making business), the lack of music courses there is a crime, given the facilities.
Every monday in the whitefriars is an instrumental irishy/englishly night,melodians, harp,violins,whistles,banjo, guitar (even a set of french bagpipes tonight) depending on people who get there, and I force a song down their throats occasionally.
The warwick folk club has splintered, and there are several 'meets'. in southern warwickshire.
Coventry itself has the Tump and Wurzel (outside cov in Brinklow) and the 'Fletch' http://www.hanmade.co.uk/warwick/diary.htm.

The four provs has singing on the stable room, but try this lot.
http://www.hanmade.co.uk/covfolk2/listings.htm