Any economics student who has studied long run cost curves should be familiar with the idea of natural monopoly. Many utilities, such as telephones, water and electricity supply are natural monopolies. This creates a problem when it come to privatizing a state monopoly, because a private monopoly can result.
In some cases the British government solved the problem by separating the natural monopoly, the network part of the business, from the supply section. So we have UK Power Networks and a number of competing gas and electricity firms. In the case of BT that was not the case and the privatized firm was allowed to keep its network. However, this may be about to change, as this article shows:
There will certainly be advantages and disadvantages to separating the network from the operator, but economic theory suggests it could be a good move.