Figures from the Fifty Thousand Homes campaign show permission has been given for 50,000 new houses and flats in the capital each year since 2014.
But the group said 36% of these were not built which was "compounding the huge challenge" of building more homes.
City Hall said the data "underlines the huge scale of the challenge we face".
The Fifty Thousand Homes campaign was launched by London First "to ensure London builds the homes it needs to stay competitive".
The group found fewer than 25,000 homes have been built in the capital each year for the last six years, compared to the 50,000 required.
"We have to act now to keep hold of the people that make London work," London First CEO Jasmine Whitbread said.
Lewisham Councillor Damian Egan said some building work in the borough, like in other parts of the capital, was being delayed by developers as they "wait and see if prices go up".
He called for the introduction of a land tax as "there's no financial incentive for developers to get building under way".
Housing charity Shelter, which has backed the campaign, called on the mayor "to get tough with organisations who have planning permission but don't get on with building".
Anthony Impey, founder of technology service provider Optimity Ltd, said his business was one of many finding it "difficult to recruit great people".
"It's really, really difficult, particularly for young people, to find somewhere affordable to live," he said.
Deputy Mayor for Housing and Residential Development, James Murray said City Hall was working to build more homes but "solving London's housing crisis will be a marathon, not a sprint."
Planning permission is being granted for enough homes to solve London's housing crisis but over a third of them have not been built, campaigners said.