It's funny you say that about the funding--I guess I've been seeing so many studentships and AHRC scholarships and whatnot that the funding opportunities for a UK student seem amazing (and the tuition not all that high at the home rate).
Therefore, I'm hoping for a miracle--to win a studentship that will offer fees plus some sort of maintenance stipend (whether in exchange for teaching or not), because that would mean that at least I wouldn't be going backward/downhill, if you know what I mean.
Unfortunately, the problem is that studentships and research grants/funding are usually only available to UK/Home fees students... and to qualify for them you must have lived in the UK/EU for 3 full years before starting the course AND have no immigration restrictions (i.e. UK/EU citizenship or permanent residence in the UK).
Quite often, foreign PhD students in the UK end up having to fund their studies themselves using savings, private loans, or taking employment at the same time, or they find funding from scholarships or sponsorship elsewhere (possibly even from the US) - but I think scholarships are pretty hard to come by.
I did my masters degree at Bristol University and when I was looking into applying for a PhD project, I didn't even bother applying to my department in Bristol. They only had enough funding for 6 PhD studentships, which were only available to UK/EU students and they had over 100 applicants for them.
Two of my friends did manage to study for their PhDs at Bristol that year, but one got her funding from NASA - she actually got a US student visa, enrolled at Michigan Tech University and graduated from there (and she was paid in US dollars as well), but she studied in Bristol as her MTU supervisor was based in Bristol. The other friend got his funding from a research institution in Belgium, so was paid in Euros.
As for which schools, I'm concentrating on Exeter and a few others.
Exeter is a good school and the city is really nice too. I studied for my undergraduate degree at Exeter
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In general what UK PhD candidates do is they apply for a certain PhD project that is being offered, and that individual project will usually have funding associated with it, as the professor will have proposed the specific project and will have been given money to pay a PhD student to work on it.
So, when I was looking for PhD projects to apply for, instead of looking at particular schools, I searched for specific research proposal fields/subjects/topics. I found one project at Oxford, one at Bristol and one at UEA. I didn't apply for Bristol because of the competition for places. I was going to apply for UEA, but the project wasn't going to start for 15 months and I wanted to start a PhD earlier than that, and I did apply for Oxford, but I got rejected. I also applied to a US school for a PhD and was accepted, fully-funded on a TA/RA studentship, even though I was an international student (I only stayed in the US for 8 months though because I wasn't happy there and I wasn't keen on the research or how PhDs worked in the US).