The economies of scale occur at such a high level of output that it is only practical to have a single firm in the industry. If there are more firms then the average cost of production will rise. We can see this in the diagram below. The optimum size of the industry occurs where the LRAC curve is at a minimum. If there were two or more firms then the unit cost of production would be higher.
Economies of scale mean that as the firm grows in size, the cost per unit decreases.
There may be external or internal economies of scale. There are various different types including marketing economies, technical economies, risk-bearing economies and financial economies. The main part of the railways that is a natural monopoly is the rail infrastructure - that is the track, the stations and the signalling equipment. It would be impractical to have that run by more than one company and so privatisation meant that all this activity was put into the hands of one company - Railtrack. Railtrack then lease the track to the train operating companies.