I think the way it generally works is that either industry or one of the research councils fund universities to undertake a piece of research, then the university takes on the role of identifying a good student to undertake the research work (since all Masters degrees involve an element of new research). There are 7 reasearch councils (where the grant has originated from central Government). This is one that deals with most science research.
http://www.epsrc.ac.uk/AboutEPSRC/default.htm
I think you start the process by talking to the university where you would like to undertake the course - you don't talk to the research councils direct. Most Masters students supplement their income by doing some paid work with the undergraduate courses - the unis know that the post-grads need to have earn a bit to have something to live on.