Provincial salaries

What is the difference in salaries between London and the provinces - say Leicester, Birmingham. Say you earn 100k in London and move to a provincial town for a similar role. The dimensions of the role and professional / technical expertise required are the same. In my mind the salary should be the same. But I expect there is a premium attached to London due to the cost of living. But that said, maybe they need to offer more to attract a London candidate to the provinces.