======= Date Modified 21 Jun 2009 12:23:44 =======
Having a UK PhD and/or a scholarship from a UK university does not alter the ability to reside in the UK once you have finished - I don't even think it puts you in any fast-track immigration system (like the US visa system for science PhDs).
If you're a European citizen (as Rick says), you have a right to live and work in the UK. If you're an international student, then once your student visa finishes, then legally you must leave the UK unless you have a work visa (i.e. have job), or your student visa is extended.
I'm not sure about the rules for Commonwealth countries, but Germaine Greer has just been on the TV this morning saying she still has problems getting back into the UK despite the fact she's lived her for decades.