Postgraduate studies - public funds?
Short Answer: Instead of looking for scholarships yourself, try to find a funding through academics and/or university in the UK. There are always funding available for talented students; and if not you can apply for a scholarship through an academic. 

Longer Answer

Ok, I did my fully funded PhD in the UK so I can help on this. Do the following: 


Find a Supervisor: First and foremost you need a solid supervisor that can help you through research, at the topic you want to work on; and understand that money is an issue. 
Funding Through Supervisor: Then see if the supervisor has some money, he/she might not have 100% of the funding but can afford less say 50%. 
Funding Through Research Group/University: Then you need to look into any funding available through the research group or the university. This might cover the rest, or close to 100% of the funding. 
Take Classes Through PhD Studies: Academics always help PhD students, if they need some extra cash, they let them to help them in laboratories and/or marking. This is not too much but at least you can get couple of meals out of it. 


Note On Location: If you can't find a funding in London or surrounding cities, try the northern cities as well. They are also cheaper to live compare to London and southern cities. 

Note On Courage: I had a hard time financially, and so many of my friends. So keep going and you shall find a funding one way or another.