The government owns 58% of RBS, and 100% of Northern Rock, both previously private banks.
Meanwhile, we pay water rates to a private monopoly. Six private energy firms control the market for gas and electricity. The railways are run as essentially private monopoly enterprises. Air Traffic control and defence research is part privatised. There has been increasing privatisation of schools and the NHS, including PFI where money for capital projects is borrowed from the private sector (at rates higher than we would have been able to borrow from the government). The telecommunication industry is completely in private hands, despite BT's dominance stifling competition.
It's a funny old world.