It's very rare to find any singing in English pubs, but Beatles, Oasis and Jarvis Cocker covers seem popular when you do get people's tonsils oiled, and the odd wartime favourite might be heard from the older folk. Tom Jones numbers go down well. Otherwise any of the standards you'd find on a Karaoke machine. One genre you'd be wise to steer clear of is traditional folk - it's not very popular in English pubs. ;-)
Seriously though, I imagine the people asking probably want a pastiche of what they imagine a trad English pub night to be, so just sing whatever you like!