LONDON, Aug 24 (Reuters) - Britain set out plans to spend £10 billion ($13.6 billion) on lower-cost housing for renters with a focus on London, although its target ‌for offering social rent was lower than a pledge made by new ‌Prime Minister Andy Burnham.

The government said around 60% of homes delivered through the funding would be for social ​rent — a subsidised cheaper form of rent that can be built by local councils or housing associations.

That was in line with the proportion set out by the government of former Prime Minister Keir Starmer, which created the programme, but below Burnham's pledge to deliver ‌all housing under the programme ⁠via local councils.

Burnham, who took over in July, has said empowering local councils to build social housing, as Britain did after World War ⁠Two, could lower the amount of the welfare bill that goes to private landlords, reduce homelessness and provide security to people on lower incomes.

"Councils built this country out of a ​housing crisis ​once before. Backed properly, and trusted to get ​on with it, they will do ‌it again," Burnham said in a statement late on Monday, which included details of the first wave of funding.

But housing minister Matthew Pennycook said councils did not yet have the capacity to take on the whole programme.

Under the first phase, the government said on Tuesday that more than £7 billion — the first tranche of a previously announced £39 billion ‌in funding over 10 years — was earmarked for ​the capital where local authorities were expected to deliver ​over half the new homes, the ​government said.

Over time, more than £16 billion of the total funding plan ‌will be allocated outside London, the government ​said, adding it ​would prioritise social rent homes and council house-building.

It said the first wave of financing would support the construction of more than 70,000 new homes.

The government said the ​house-building programme would advance ‌another policy priority of Burnham — devolution — by giving mayoral authorities the power to ​set strategic direction in their areas.

($1 = 0.7335 pounds)

(Writing by William Schomberg; Editing ​by Muvija M; Editing by Sharon Singleton)