But they do have a virtual monopoly on direct broadcast by satellite for the UK.
BT or anyone else can't send up a satellite and compete with sky.
https://en.wikipedia.org/wiki/British_Satellite_Broadcasting
I believe, but can't confirm before most of the cable TV companies merge into Virgin, once an area had one service in it a rival couldn't enter that area in most cases. London begin a rare exception. It may have been down to local planning.
Though due to the cost, once one area was covered there wasn't likely to be enough of a market to support two cable networks in the same area even if it was allowed. So an effective monopoly even if no legal barriers enforced it.
BT's share holders didn't get their network for free, they had to buy the shares from he government, which at the time was largest share issue in the world and that was only just over half the company. The remaining share were sold off later on. So I'm not sure if cheap is correct, I don't have time to workout how much investors would made on the shares if they still have them now.
Large parts of virgins network was given to creditors in shares of the original companies that almost when bust, they could probably be classed as cheap as the BT Shares.