Hey, sorry to hear you didn't get an Oxford offer, though congrats on getting offers from your other four! Some outstanding music departments in that list. You should be extremely proud!
My advice would be to firm/insure unis you currently have offers from - perhaps unis that have lots of ensemble opportunities for you, and options for examined performance modules in the course? Does Durham have college orchestras, due to its collegiate nature, as well as uni-wide orchestras?
If you enjoy academia, you might end up feeling under-academically-challenged at a conservatoire (though of course performance standards there are incredibly high!), so I'm not sure it's worth you taking a gap year
just for conservatoire applications.
Even though I'm a muso, the only uni I applied to that you've got an offer from is KCL (and I applied in 2006, so my info would probs be outdated anyway!). I insured KCL without seeing it, and regretted making that decision a lot when I went to their open day. At that time, the snobbish atmosphere there really put me off. Have you been to in-person open days at all these four unis, and have you looked at the course content and structures of them? This can be a good way of narrowing things down

Dependent on what your principal instrument/voice is, I'm not convinced it's worth taking a gap year to reapply to Oxbridge when you've got some wonderful offers to choose from

Good luck with whatever you decide to go for!
TLG