The research, commissioned by London Councils and carried out by PricewaterhouseCoopers (PwC), examined how much cash public bodies could save by using the Total Place approach to services, which is currently being trialled by the government in 13 local authorities.
Closer working between health and social services on chronic care cases in the capital could save more than £800m for every £5bn budget, the report found.
Cash could also be saved if local authorities integrated youth offending teams with local youth provision, education services and drug and alcohol teams, the report said.
It suggested the Youth Justice Board, the Home Office and the Department for Children, Schools and Families give councils a series of grants to tailor spending to local priorities.
This would allow councils to identify children at risk of offending and offer them intensive support early on, the report said.
£73.6bn of public money was spent in London in 2008/09.
Currently local authorities have no control over the 156 quangos responsible for £5.6bn of the city's annual public expenditure bill, nor do they have any say over the £25bn spent by central government departments in the capital.
PwC estimated that public bodies in London could save almost £1.6bn, by devolving cash from quangos to local bodies.
London Councils' chairman, Merrick Cockell, warned the local government funding system is flawed.
"The way public bodies are funded, and the number of different organisations working for similar or overlapping aims, unfortunately make waste inevitable," he explained.
"However, PwC's research has shown us a way to radically reduce London's burden on the public purse - while still improving the services we offer Londoners. Amidst the ongoing debate around the public sector funding squeeze, we will be thoroughly examining their conclusions in the hope of setting out significant reforms for the capital in the coming months."
Total Place is a new initiative that seeks to identify and avoid overlap and duplication between public bodies to save cash across central and local government.
