Regulation. Regulation regulation regulation.
I too believe that free markets are the solution to a great many of the conundrums of organising a society, but I also believe that a strong and socially conscious (by which I mean its prime directive is the enhancement and improvement of living conditions for all of those under its jurisdiction) regulatory hand is necessary.
The U.K. has plenty of regulations, and toothless enforcement of practically all of them, to the extent where ignoring them and the ensuing fines are just a cost of doing business.
With firm regulation, a free market could operate both profitably and fairly to run public services.
As long as there’s a commingling of commercial and political interests, however, this is an improbable reality. The changes would have to start in the culture of government.