How is Privatisation a Free & Fair Market?

I agree with the economic argument for free & open markets but I disagree that privatisation has lead to any of these. Take the trains for example. I travel to Nottingham regularly. I can only get 1 service to Nottingham from London within reason. The ticket from London to Nottingham is far more than 2 tickets, 1 from London to Leicester & the other from Leicester to Nottingham even though it results in the same journey. The train companies say I can not buy these tickets without leaving the train. This is not a free and open market.