Hey! Sadly the graduate in question has not responded... I will try to message someone else if I can remember (got lots going on atm).
In terms of referees, I think it helped that my referees were quite senior and prestigious people. One of them (after and before teaching me, not at Oxford) had been a fellow of All Souls College, Oxford not once but twice. Yes apparently that can happen! But obviously they also need to know you well enough to say nice things about you. Regarding funding, what I was trying to say was to tell the referees in your communications that you are seeking funding and so their assistance would be very gratefully received, so that they get the hint that you would appreciate a glowing reference from them to help you get it. If they've got half a brain, which I assume they do, being referees, they ought to take the hint.
Meanwhile, other things that I think improve your chances of getting funded are:
1) The research proposal. It should be sexy (that's what an English graduate student at Oxford told me before I applied). By 'sexy' I mean topical, important (it can still be niche, but then try to link it to Big Issues, whatever they are in English studies), original, relatively under-examined, and last but not least, playing to your strengths. Why should YOU research this? What is it about your aptitudes, skills and background which make it appropriate for you to do? My research was closely aligned to my professional work after I was an undergrad, so I was able to talk about why I wanted to do it.
Having said that, the research element counts for less at Oxford than at Cambridge. Remember Cambridge interviews, unlike Oxford, so be prepared to explain all this coherently at interview. I like to think I explained it quite well, and Cambridge did offer me funding as well, so I think that made a difference.
2) The transcript. Yeah, no ****, have a good transcript. And be prepared to shout in your application about your dean's list/departmental prize/etc. I think I spelt out in my statement the high mark I got on my extended essay, although it was on my transcript already. Don't be ashamed to big yourself up. Eyes on the prize.
Oh, and you asked if your current uni makes a difference. I don't know for sure, but I do know that some other master's students at my college came from non-Russell Group unis, so I'm sure it's not a Russell Group clique - I think your individual performance as a student counts for more. An outstanding student from Lancaster is unquestionably better placed than a mediocre one from UCL or Birmingham.