Sadiq Khan has rubber stamped Hackney Council’s £384million Britannia Leisure Centre redevelopment project, effectively ending campaigners’ hopes of stopping the work.

Councillors had signed off the controversial scheme earlier this month and it was passed over to the Greater London Authority (GLA), which has final say on major developments.

Save Britannia Leisure Centre campaigners, who had been fighting the plans since they were announced more than two years ago, had written to the mayor of London urging him to reject it.

They argue the flattening of their cherished leisure centre to make way for “state-of-the-art” replacement, a housing development and a new school will drive more families out of the borough, take away green space and create pressure on public services.

They also say the council will struggle to sell the private homes – which make up 400 of the 481 total. They will be built last and are financing the rest of the project. Some 4,534 people signed a petition against the plans, which were also opposed by Anthology – the developer who redeveloped the neighbouring Colville Estate with the town hall.

But the plans were waved through regardless. Mayor Phil Glanville welcomed the final approval, saying the council could now get on with building the homes.

“It’s fantastic this ambitious scheme has been approved,” he said. “Hackney needs improved leisure provision and hundreds of more school places. I’m very proud that, despite ongoing government cuts to our funding, our council is finding innovative ways to keep investing in our communities.

“It’s taken us years of planning, consultations and public meetings to get to this stage, and we’ve listened to residents and taken on board their feedback throughout. We’ve tried to include as many elements of what people have told us they want as possible.

“The current leisure centre simply doesn’t deliver the standard of provision or access that Hackney’s diverse communities expect, need and deserve now and in the future. The new centre will be better in almost every way and preserves many of the family friendly elements we know that people value.”

Work will start early next year and the leisure centre is expected to be completed in 2021. The existing centre will be open until then.