I'm too late to really contribute but yeah - your info is very out of date. The BBC built and maintained their own transmission infrastructure until about 20 years ago. There was also another independent network used by the other broadcasters - there was a lot of overlap and cooperation between the two but essentially they were separate. Either way both moved into private ownership and now the network has been consolidated and is operated by Arqiva. The license fee does not directly fund this.

The license fee is largely used by the BBC but there are other recipients and there is nothing to prevent the government from deciding that they shouldn't get as much. A quick google took me to the TV licensing website where it clearly states: "Part of the fee also contributes to the UK broadband rollout, funding local TV channels and S4C, the Welsh language TV channel, as was agreed with the government as part of the 2010 licence fee settlement."