[Stooky Bill]

Can't remember where I read this but because the tower was instrumental in TV transmission back in the day (it probably still is) is it true its actual physical location was effectively a state secret?

Not just TV, it was the centre of the Post Office's microwave network so carried inter-city telephone calls as well as television. The telephone network was probably considered the more important traffic.
www.dgsys.co.uk 
It was built on the Museum telephone exchange, which is still there
www.dgsys.co.uk 

The tower itself isn't used for much any more, all the dishes and horns are gone and although there's still some aerials on it they're localised transmissions.... there's a DAB transmitter on the roof for example.

It's what goes on in the buildings at the base which is important and this is what is referred to as the tower operationally. When you need to contact BT for a switch you phone 'the tower', the colour bars have 'BT Tower' on them.... but that's nothing to do with the actual tower.

BT still has a role in television, most big TV facilities have 'local end' connections to and from Tower and BT provides the contribution networks for both the BBC and ITV. That wasn't always the case, BT only got the contract with the BBC about 6 or 7 years ago.

However these days these are big MPLS fibre networks, so although the control system and people you phone are possibly based in Tower the route the data will take probably goes nowhere near it. IP changes everything, hence once the traditional phone network goes next year there'll be need for a lot of their exchanges.... It's all in the 'cloud'

Since deregulation in the 80s you don't have to use BT to get video, audio or data from a to b. Arqiva have their own network, Globecast do a lot of TV connectivity and telecoms companies like Vodafone and Virgin Media have large networks. The advantage with BT is that they through Openreach have fibre presence literally everywhere as a legacy of the old monopoly days.