The Resolution Foundation and IPPR think-tanks said the suggested rate of £7.45 an hour and £8.55 in London would add £6.5bn to workers' earnings.
Paying the living wage in the public sector would increase costs, but would save the Treasury more than £2bn, the study found.
The think-tanks said Whitehall departments and London boroughs should pay the living wage, which is higher than the £6.19 adult national minimum wage. About five million people earn less than the living wage.
Kayte Lawton, of the IPPR, said: "As a first step, making sure that all council staff in London are paid at least the living wage wouldn't cost very much but would be an important symbol of political leadership. Councils in other parts of the country, like Glasgow and Newcastle, have shown that the living wage can be affordable even though the costs are higher."
TUC general secretary designate Frances O'Grady said: "This report shows that fairer wages and decent in-work benefits are both vital means to boost living standards for millions of workers in low-pay Britain.
"Becoming a living wage employer helps staff, improves a company's reputation, and in many sectors is easily affordable. In some cases introducing the living wage leads to overall wage bills rising by less than 1%."