The Telecom Tower is visible from most of London.
I suspect that there are many others like me, who still think of this as the Post Office Tower, which it was until British Telecom was spawned from the Post Office. Although public access has been restricted to the tower since the bomb in the early seventies, and stopped in the eighties, the revolving restarant is still used by BT for corporate hospitality (I got invited once!).
The communications dishes are mostly unused these days, but they can't be taken down (or added to) without permission, because it would change London's skyline so much. This site has a great history and virtual tour.