Greater Manchester Mayor Andy Burnham recently urged the government to permit Labour mayors set local income taxes in England.
The plan would let regions across the country retain more funds for schools and hospitals.
Critics say this could create unfair tax gaps between areas widely.
Burnham argued local leaders clearly understand what communities need most.
In Wales, some officials many are concerned these ideas could proliferate if the UK breaks up tax decisions.
Politicians across the political spectrum dispute whether local control supports or damages fairness.
The fight now shows how far Britain will reallocate control of finance and services.