Finding finance can be extremely difficult. The possible funding body depends on the subject, so find out which one deals with what you want to do, and the correct application procedure and deadlines. There is a list of the main grant giving bodies below. Addresses may be found in any of the books mentioned in Further Information. If the 'official' funding body for your course refuses you, you can't apply to another one.
Some courses attract no funding at all.
If you don't get funding, you will have to find the fees as well as your living costs. Fees vary, but are often around 2,700 a year for UK and other EU nationals. There are a number of different funding bodies. Ask the academic department to identify the right one for the course or research you want to do and follow the appropriate procedure. To be eligible for an award, you have to be resident in the UK, not for the purposes of education, for three years before your postgraduate study begins.