The Keybridge House Development is a mixed-use scheme with private residential flats in two towers and a series of mansion blocks, with restaurants and shops at ground floor level, alongside a new primary school.
Architect Allies and Morrison designed the complex which would boast the tallest brick clad building in the UK, echoing many New York high rises.
The main building will rise to 128m, replacing the existing 1960s telephone exchange building at the site in Vauxhall. It will be accompanied by a shorter 21-storey residential tower rising to 73m.
BT is expected to put the site up for sale once it has achieved planning permission and decommission the building next year.