If all the UK regions like Yorkshire, London and Lancashire competed using only local players, who would win?

Good question, You could ask which region North-West, North-East, etc has produced the most England Internationals.

I would like to say the North-West.(But I am biased)

Difficult one as most of the major regions have multiple pro teams competing. London produces a lot of good players, but also has more clubs to compete for those players. Newcastle would do well as there is minimal competition for players (Sunderland being in League 1 and the only other pro team being Gateshead). Manchester United/City would do well again because of them being the only real competition to each other. I can see Leeds doing really well again due to more player choice.