Water companies in the UK operate under regional monopoly, so most people only get a single company they can buy water from.

The free market approach seems to require allowing water companies to even build and maintain parallel infrastructure that can't be shared, if they consider it to be economical. That would require immense capital investment, meaning the barrier to entry would likely be very high. The "efficient" case, where joining an existing pipe infrastructure is cheap, due to competition, would entail having several parallel networks of pipes running between reservoirs and people's homes. This was viewed as profoundly wasteful, even by the Thatcher government that privatised water, and that's why it's forbidden by regional monopoly.