PhD funding source for international student in the UK
Your best bet is probably to check if there are fellowships available for study abroad from your home country. However, depending on where you're from, there may be special programs available. For instance, there are Commonwealth Scholarships available for people living in members of the British Commonwealth.

There are some databases of UK awards for general students: here, for instance, is a list of postgraduate scholarships available to citizens of any country.