Council leader Kieron Williams was responding to a question from Old Kent Road ward councillor Richard Livingstone at Wednesday's Southwark council assembly meeting.
"I think it is absolutely a question of 'when', not 'if'," said Cllr Williams.
"I'm delighted to say that work is currently under way to put together the detailed updated business case for the Bakerloo line that will be coming out next month and it's looking really positive, having seen an early copy of it.
"And I'm also delighted to say that I've now secured that every single council in London has backed the Bakerloo line in their London Infrastructure Framework."
Turning to the benefits of extending the Bakerloo line towards Lewisham and beyond via the Old Kent Road, Cllr Williams said: "For Southwark it's about 20,000 more homes, and about 10,000 new jobs it will be creating, as well as all of the additional investment: more local CIL (community infrastructure levy), more strategic CIL to invest in the things that matter to our residents.
"But I think it's important to say it isn't just a Southwark project. This is a London project and for London it will deliver 110,000 homes and 130,000 jobs.
"It's the kind of investment we need to keep our city growing and I'm delighted that we're making progress.
"We've got work on site at Elephant & Castle on the new ticket hall, we've got the safeguarding in place for sites along the Old Kent Road, we've got TfL working on the designs for the tunnels and how they can be extended.
"It's a project that is is about the future of this borough and the future of this city."
In the latest edition of Southwark Life magazine the council confirms that plans for a 'Bakerloo bus' express bus link along the Old Kent Road - first mooted more than 18 months ago - are still in the works.