Royal Academy of MusicWatch
RAM has a large emphasis on the technical elements of music, hence why they want piano as well. It won't hurt to apply there, but maybe apply to a couple of music degrees at universities as well as conservatoires.
Just from my own knowledge, most universities don't require grade 5 piano. The only on I can think of that does is Edinburgh. I'm going to Surrey in September, and got other offers too: none of them wanted grade 5 piano.
This is a list of all UK conservatoires. Have a look at each one and see what they want from you. I got into LCoM last year, but declined (you might love it though, so don't rule it out) and I have a mate going to Guildhall in September. Neither of us have grade 5 piano. It could be that it's only for singers.
Also, I couldn't find anything on the RAM website that said it required grade 5 piano, so it may be worth double checking that information.
Either way, good luck! I hope you get where you want to go