The BT Telecom Tower is not a tourist attraction as such; it has been closed to visitors since the IRA had their dirty way with it in 1971. However it is an iconic landmark, looks cool, and stands for London.
The BT Tower was formerly known as the Post Office Tower and has featured in TV programs including Not the Nine O'Clock News and Doctor Who. Harry Potter flies over it in his magic car in The Chamber of Secrets and the tower is blown up in V for Vendetta.
As British as fish and chips, the tower is a marvel of engineering but not really worth a visit. Think of it as part of your London life, an ever present, 70s throwback that sits in the corner of the skyline.