English folk clubs boil down to two basic formats:
1. Staged performance - ranges from planned concerts to open stage
2. Singaround - ranges from fairly formal around the room sing/play through to open jam session.
Atmosphere and range of particpants will differ between the formats.

Most tend towards a middle aged, middle class demographic.

If you are depending on public transport then London may be your best area as services generally run until after midnight and there are good 24*7 bus services on the major routes. Check out Folk London for a list of clubs.