I don't know if they are all abandoned, but the microwave network they supported is no longer in use, which is why they no longer have visible horns or dishes. This is also true of the PO/BT/Telecom Tower in London.
They were built in the early 60s, essentially for the Backbone military comms project which transferred air defence radar plots from around the country to UK and Nato command bunkers. Backbone was also used to communicate with various military and government bunkers, who could join the network by emerging from their holes in the ground and inserting a temporary antenna into the microwave beam. Their basic structure was designed to survive a near miss from a nuclear warhead, though obviously they wouldn't be functional without repairs.
(I think this is all declassified now
)
Civilian users did use Backbone as there was normally massive excess capacity. The Post Office used it for telephone circuits, and the BBC/ITA used it to distribute TV services.