One reason was to increase investment. In water's case the infrastructure had been under-invested in under public ownership for decades, due to it always being a low priority from a political point of view.
The regulatory structure of the privatized industry says the water companies can only make profits if they make capital investments, and so the amount invested in water infrastructure in the UK (particularly England) has duly gone up a lot since privatization and has been comparable or higher to other nations since.
From this point of view, it's less about choice and markets as a way to structure the regulation and ownership so that capital investment actually happens.
Privatisation increasing investment means one of two things, either the investors are getting ripped off or they're going to get a profitable return on their investment. Assuming no government would admit to the first and no investor would intentionally invest in the first, let's assume the second is the plan. In which case, if the investment will yield profits, there's no reason the government shouldn't make the investment themselves so that the public get the profits (as well as the benefits from increased investment at the start).
The regulatory structure of the privatized industry says the water companies can only make profits if they make capital investments, and so the amount invested in water infrastructure in the UK (particularly England) has duly gone up a lot since privatization and has been comparable or higher to other nations since.
From this point of view, it's less about choice and markets as a way to structure the regulation and ownership so that capital investment actually happens.