I imagine that most of the labs you find on this site would accept you for a PhD if your qualifications are good enough. The problem you will face is finding funding. Fees for overseas students are roughly double those for home (UK) students. Some grants are available to cover the difference between home and overseas fees, but this would still leave you owing at least £3000 per year plus living expenses (which are high in the UK).
If you find a project on FindAPhD which is of interest, but is not marked as available to international students then visit the web site of that university and search to see which funding schemes they may have available. Do not write direct to the supervisor as they receive so many requests from international students asking for projects with funding that they often don't bother replying.
The first place you should look for funding is through your home country’s Department of Education (even if they don’t fund overseas study, they may know what other schemes exist). For study in the UK you should also try the http://www.britishcouncil.org” target=_blank>British Council (in your home country, don’t write to the one in London). For study in the USA try the http://exchanges.state.gov/education/fulbright/commiss.htm” target=_blank>Fulbright Commission.