I don't know enough about Russia to have a helpful opinion on Pussy Riot. But I think it is an interesting question to ask what would have happened to similar campaigners in the UK who performed punk songs criticising David Cameron in the same type of places.
I imagine that they would most likely have been charged with aggravated trespass for their earlier performances (on the metro, on top of buses) and probably fined (maximum penalty £2500 fine or 3 months in prison, but more likely £2-300 for first offences).
But of course for any protests within the designated area around parliament there are potentially more serious penalties (up to 51 weeks in prison).
Performing in say St Pauls - well, I guess we've seen from Occupy that the Church authorities after a bit of a wobble were reluctant to be seen to be prosecuting activists. I don't know if that would still be the case if they were anti Church, but I suspect probably so.
No doubt by this time the band members would find that they had personal police attendants following them around a lot of the time, and definitely present if they went near any significant sites. On previous form (not only the recent cases, but going back at least to the 60s) then the Met also would probably have managed to place an undercover officer in any movement that they were a part of.
So I guess overall less severe consequences than Pussy Riot have faced in Russia, but certainly not trivial.