@thatfineframe
0404343m is right about advising you to spread your net wide, since you already have Oxford on your CV you really don't need to worry about prestige. Not only have quite a few academics told me that it looks better to have more than one university on your CV, but also that having AHRC funding is considered more prestigious than Oxbridge and no funding.
My advice would be to get in touch with your tutors at Oxford in the areas you're interested in and ask them which academics at other universities would be suitable supervisors, then you can get in touch with them too. They all understand that funding is often make or break, and actually students are the big beneficiaries of the BGP system, because you can apply to more than one place, previously in the open competition you had to put all your eggs in one basket.