A large number of charities and trust funds offer funding to students at university level, some of which is available to intending postgraduate students, and some to students who have already started their course (this is more common for PhDs and other doctoral study).
Funding is usually awarded on the basis of two main criteria: either academic excellence, economic hardship, or both. Individual charities may well have additional criteria which relates to the work of the charity itself, and there are sometimes other strict eligibility requirements based on subject or place of residence. The funds provided normally relate to the amount of money a particular charity or trust may have, and can vary in amount from a few hundred pounds to several thousand. They are frequently intended to be partial funding only, so you may find you need to apply to more than one source if you need funds to cover all your study.
Some of the charities and trusts date back several centuries, and these usually have some sort of historical affiliation with a place or particular organisation, such as the City Livery Companies. Sometimes, funding is offered through named scholarships and sometimes for specific courses or study only at selected institutions. Smaller charities' funds may be administered through larger organisations, including the British Council, and various Local Authorities, so it is always worthwhile checking with your Local Authority.
Larger schemes or charities include the British Council, the Wellcome Trust and major academic subject associations and learned societies that may have an educational trust as part of their activities. Some banks or other large organisations or commercial companies of long standing also have educational trusts.
PostgraduateStudentships carries descriptions of main schemes and awards offering £1,000 or more in the funding database.
You can start looking now for Masters funding and PhD funding.
Try this: If you browse to your subject area, you can filter the results to show the charity funding only, and then browse through those to see which funding you could be eligible to apply for.