If you are an EU student from outside of the UK then there aren't so many fully funded studentships available. Most UK research council studentships only pay fees for residents of other EU countries.
If you have been ordinarily resident in the UK for the past three years for reasons other than full time education then you should qualify for a full research council studentship.
The good news is that other studentships do exist which are available to all EU (and some other European) nationals. Particularly in biology/biomedicine, which probably has more funded PhD studentships than any other subject area. For example look for Marie Currie scholarships, European Science Foundation sponsored programs and EMBL related schemes.