For many years (decades, in fact!) it was administered by the Radio Regulatory Dept. of the Home Office (HQ was Waterloo Bridge House for anyone who knows London). They were basically under the ultimate control of the Postmaster General, who was also in charge of GPO Telephones.
Like many other well-established govt. bodies, it all changed in the 1980s and radio got passed around like a grenade with the pin removed!
Control finally settled with the Radiocommunications Agency, which was set up as a new branch of the DTI (Dept. of Trade & Industry). Don't you just love the alphabet soup of government?
Anyway, they have a website:
www.radio.gov.uk There has long been cooperation between the U.K. and neighboring countries on frequency allocations, under various international agreements with the Intl. Telecommunications Union and the European Broadcasting Union. (By the way, the latter is nothing to do with the EU or the EC Commission, although like everything else I don't doubt that that bunch of undemocratic bureaucrats would try to take credit for it!)
We do occasionally get some interference from the Continent, even up in the UHF range. Here on the east coast I can sometimes receive UHF TV signals from The Netherlands, and co-channel interference appears on shared channels, but it usually doesn't last long. I should add that under such conditions we also get co-channel signals from other UK transmitters.
Tne south coast can occasionally get similar co-channel signals from northern France, although because the French system is incompatible with ours most people wouldn't actually realize the source of the signals.