Have you checked to see if the NHS has any specific rules against funding non-EU residents? You are eligible to receive funding regardless of how long you have lived here, but some institutes impose their own residency rules.
Either way, you will still have to pay international student fees at the University.
You should also check that the funds cover tuition for international students. They might only fund home tuition rates, and offer you the option of covering the rest.
For instance, I work for Imperial College as a researcher. My boss really wants me to start a Ph.D. with her for which I would receive a University funded stipend. However, because I haven't been in the UK for three years, I would still have to pay international student fees at Imperial which is considerably higher. (Needless to say, I can't afford not to wait)
