The chart below shows that while inequality in the UK rose under Thatcher, the poorest families saw virtually no increase in their disposable income over the same period. So much for the theory that making the rich richer will make everyone else richer too.
Under Tony Blair, inequality stabilised, but the incomes of the poorest rose significantly. Both these trends were due to redistribution through the tax system. Had the government not intervened, inequality would have risen further and the poorest would have seen far less improvement in their incomes.
The current government is about to cut tax credits significantly, which will hit the poorest the hardest once again. So much for compassionate conservatism.