Hi. I'll try to help. It is not generally good news though, I am afraid. You don't say if you're planning undergraduate study or postgrad study but I'll answer anyway.
First the bad news:
Unfortunately, assuming you are not from Europe, there is an almost negligible chance of receiving an undergraduate (or postgrad) scholarship at a UK university that will pay both your fees and give you a stipend. Really, I think you would be exceptionally lucky to even find one which pays even just the fees.
If you were exceptionally lucky you may find some contribution towards your fees or a small contribution to your living expenses, but both of these are rare and especially rare for international students from outside the EU.
International students from within the EU for PhD funding were previously only entitled to fees only studentships from the government research councils, however this is now changed to include the basic stipend as well. There are relatively few research council funded studentships each year however. (STFC, which does astronomy, particle physics, etc) offered 300 this year. These places can be very competitive. If you're not from the EU this route is not open. Still, if you are from the EU and want a PhD this is the best funding route.
You don't say if your £20000 includes fees or not, but there is no chance of receiving a £20,000 stipend, sorry. The best PhD stipends in the UK currently top out at ~17k and typical is £12,600 + fees. These are only for EU and home students however, and only for postgrads. £12,600 is quite livable if you are reasonably frugal.
Your working hours will also be restricted on a student visa too, so funding via working is practically impossible as well, sadly.
Good news:
1) Occasionally a department will come into some money and offer a postgraduate international fees scholarship. You will need to contact each department individually to find out if they have any. The best time to do this is between October and December the year prior to when you wish to start. Be nice and talk to each department individually.
2) Despite all the negativity, the British Council (search for them online) may be able to help you further.
3) Nothing is impossible, so if you really want it, keep trying, perhaps an opportunity will be presented. :-)