Those ideas of privatization of the 80's have nearly always come to the same result: private companies dealing with public services make them of lower quality and more expensive. Just the opposite they were supposed to become. Not only transportation, but communications, education, health, mail...
The main purpose of a company is to make money, which is ok, but that is fairly incompatible with giving quality and good prices.
But, on the road of becoming private, some good money went to the pockets of few people near the power.
Before 1948, all railways in the UK were in the hands of private, profit-making companies, and (save for the unfortunate effects of the Second World War), British railways were of extremely high standard and the envy of the world. It was private money that built the railways, and the state that partly destroyed them in the 1960s with the "Beeching Axe". Politicians are no more likely to act in the public interest as opposed to their own interest than businesspeople. Both politicians and businesspeople have some incentive to do things that benefit others by means of feedback mechanisms: politicians have elections, businesspeople must satisfy their customers in order to make a profit. However, whilst, with politicians, elections occur once every four or five years and involve a single choice about every issue all at once (where all but what are perceived to be the most important issues of the day have little or no effect on the outcome of elections), businesspeople's feedback is constant and related specifically and only to their area of control. The government can get away with running the railways badly as long as it can convince the electorate that its overall policies are less bad than the opposition's. A business does not have this luxury.
Further, the state, unlike a private enterprise, has the general coercive power of lawmaking which politicians can and readily will abuse for their own short-term interests. The more that the state controls, the more that falls within the sphere of this potential abuse of power. A good example of this in connexion to railways is that, in the 1960s, following the Beeching cuts, a number of private enterprises wished to re-open some of the closed lines for profit. If they had done so, they would have provided a very useful service to people who lost out to the state's recklessness at a net benefit to the treasury. They were forcibly prohibited from doing so by the state because the government of the day did not want to be embarrassed by the prospect of being proven wrong about the wisdom of the Beeching closures, and the unions, who had a disproportionate influence on government policy, did not want the possibility of there existing railway operators over whom they had a less disproportionate influence than the state, paying the market rate rather than an artificially inflated rate for the services of drivers, etc..
As to present day railways in the UK, the state still has a controlling influence. The railways are not privatised at all, but franchised: the state contracts with private companies to run specific services for a set period on very rigid conditions stipulated by the state on infrastructure provided by the state. The companies have no incentive to invest for the long-term because they are not guaranteed to continue to have the right to run trains past the end of their franchise term, the state continues to be in a position to abuse its power (and, for example, award a franchise to the company who promises to pay it the most money in return for doing so, rather than the company that is likely to provide the best services, as is demonstrated by the recent awarding of the West Coast franchise to First Group rather than Virgin Rail), and the state continues to own all the infrastructure, which means that there is no private investment in infrastructure, and all the perverse incentives that go with the disconnexion of the infrastructure from the operations. It is interesting to note that the advantages of having the trains run by the owner of the infrastructure was recognised as long ago as the 1820s, and why in the 1990s it was thought fit to reverse that position is thoroughly obscure (and yet another example of abuse of state power).