There really isn't such a thing as an 'exact centre' - the UK is not shaped so as to have one. Depending on what factors and assumptions you put into your calculations you'll come up with different answers.
scubadiver was close with Haltwhistle. It all depends on how it is determined and measured, but I think there is a general consensus of opinion that the centre of the British Isles, is in fact a small village known as Allenheads It is situated at the head of the Allen valley (hence the name) in Northumberland, near the borders of Durham and Cumbria.