TfL's planning boss made the comments at a meeting of the London Assembly budget & performance committee on Tuesday morning.
"If you look at the Southwark planning committee agendas there's a steady stream of high density developments that are seeking planning permission on the Old Kent Road," said Alex Williams, TfL's director of city planning.
"So whether we like it or not, there is likely to be substantial amounts of additional housing on the Old Kent Road
"Our issue is that, without the Bakerloo line, that will struggle to be served from a transport perspective.
"So with Southwark and the GLA we are looking at what is the appropriate cap – probably around 9,000 units – but anything beyond that – because the [opportunity area planning framework] talks about 25,000 units – that's when we need the Bakerloo line extension."
Mr Williams said that in the Old Kent Road TfL was "trying to put the brakes on" development, in contrast to other parts of London where developers needed to be enticed to build.
He added: "Having said that, we are working very hard on it and we will consult again on refinements later this year."
Next week Southwark Council is due to consider plans for 724 homes on the Southernwood Retail Park (Argos and DFS) site in the Old Kent Road. In March, councillors approved more than 1,100 homes on the Cantium Retail Park (B&Q) site.
Last week Florence Eshalomi, London Assembly member for Lambeth and Southwark, questioned the Mayor of London about the impact of Brexit and the Government's comprehensive spending review on projects like the Bakerloo line extension.
"The paralysis in Government is causing big problems for infrastructure in London," said Sadiq Khan in his reply.
At the end of March Cllr Johnson Situ, Southwark's cabinet member for growth, development and planning, said: "Southwark Council has been campaigning for the Bakerloo line to be extended down Old Kent Road both to improve transport for people living and working in the area, and to deliver much needed new homes.
"The Bakerloo line extension will enable the delivery of thousands of new homes, including social rented and intermediate homes.
"We are continuing to push for three stations along the Old Kent Road, including one at Bricklayers Arms."
He added: "Last year we launched the Back the Bakerloo campaign, asking residents in Southwark and beyond to sign up to show their support for the extension. The campaign has been a huge success, with over 16,000 people already signed up."