I appreciate that this is not the type of question Askhistorians normally answers, but I would very much appreciate some advice from those who have already been through the PHD application experience. Specifically those who have successfully applied to a branch of the UK Arts and Humanities Research Council.
Thanks in advance.
Not exactly who you asked for, but as an unsuccessful applicant for AHRC funding (at six different universities, no less!), there's not a huge amount of tips I could give you which you wouldn't have heard before.
Get your grades right; to be in with a serious shot, you need a I:1 at undergrad and a distinction (70+) at MA. I was told several times that my 69 at MA level (I was applying after having taken a year out) would hurt my application and it proved so in the end. If you're applying while still in the process of your MA, make sure you've got at least one referee (preferably whoever will be supervising your MA dissertation) who has seen some MA level work and will predict you a distinction.
Get your proposal spot-on. Revise it, revise it, revise it. All the various AHRC consortia have different application processes, so what I did was had a 1000-word base version, which I adapted to each application. Get plenty of outside feedback - especially from your proposed supervisor at the place you're applying to. Ask to see proposals from previous applicants from your department (most PhDs will be happy to share).
Might seem obvious, but get in touch with any potential supervisors well before the deadlines (about now is the right time to initiate contact). This will make sure that they're actually available to supervise you, as well as meaning you'll have a source of feedback and someone to vouch for you within the department.
Off the top of my head, those are what I'd recommend. There's not much else you can do really; the competition is absolutely brutal. I know there are some other (more successful) applicants hanging around among the medievalist flairs here - hopefully one of them might be able to provide some extra advice.
Best of luck and obviously if you have any more questions just shoot!