A housing minister has rejected suggestions that Andy Burnham has failed to his keep promises on council housing, as the Government unveiled a nearly £10 billion plan to boost “genuinely affordable homes”.

The Prime Minister has pledged to carry out the biggest council housebuilding programme since the postwar period, with more than 70,000 homes, 60% allocated for social rent, to be delivered across England.

However, Mr Burnham has faced accusation of watering down his ambitions after he previously called for the entire £39 billion social and affordable homes programme to be spent on council housing.

During his campaign to become the MP for Makerfield, he said: “There’s £39 billion allocated over a 10-year period … I’m saying that should be dedicated to council homes.

“Let’s not be coy any more.”

Asked whether he accepted that Mr Burnham had failed to keep promises made in the lead-up to the by-election, housing minister Matthew Pennycook told BBC Breakfast: “No, I don’t.

“I mean, Andy Burnham said in the by-election that he wanted to see more money spent on social rent on council house building.

“That’s exactly what we’re doing through this initial wave of funding.”

More than £2 billion of the first funding allocations are expected to be spent in mayoral areas outside of London as part of the Government’s broader devolution agenda.

Mayoral strategic authorities are tasked with setting the strategic direction for programmes in their areas, helping to ensure investment reflects local priorities, the Government said.

The allocations are the first stage of the 10-year programme, with more than £16 billion remaining to be distributed outside London.

In addition, the Greater London Authority intends to make at least £6 billion available through the programme, the Government said, with councils in the capital expected to deliver more than half of the homes planned.

Mr Burnham said: “No child should be raised in a hostel room and no family should wait 10 years for a front door of their own.

“I have said from my first day in this job that everything starts with a good home.

“Nearly £10 billion will go to councils and housing associations to build genuinely affordable homes, most of them for social rent, in the places where families are waiting longest.

“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.”

A breakdown of planned activity by strategic partners shows 4,400 homes are set to be delivered in Greater Manchester with a spend of £529 million while 3,200 new homes will be delivered in the West Midlands at a cost of £409 million.

The North East has been allocated a £445 million estimated spend to support delivery of 3,400 homes, with West Yorkshire receiving £441 million for 4,000 homes.

Liverpool City Region is set to deliver 3,100 homes supported by £380 million while South Yorkshire has been allocated £249 million to provide 2,200 new homes.

Housing Secretary Angela Rayner said: “Families can’t be left raising children without a place to call home and none of us should spend years waiting for somewhere safe and affordable to live.

“I know how important fixing this is – because I’ve been there.

“A safe and secure home was the foundation for a better life – I couldn’t have got to where I have today without it.

“That’s why the Prime Minister and I are doing everything we can to get councils building once again – it’s fundamental to turning the housing crisis around, helping families out of temporary accommodation and into a secure home.”

The Tories said funding had been “backloaded” to fall outside the spending review and this Parliament, “meaning Andy Burnham will never have to pay for it”.

Shadow housing secretary Sir James Cleverly said: “This is a sleight of hand under Labour, and yet another unfunded spending commitment.

“The small print shows homes won’t have to be delivered until 2039.”

Liberal Democrat housing spokesperson Gideon Amos said: “The move to allow councils to bid for funds for social housing is a good first step to helping secure adequate housing stock.

“However, until they address the care funding crisis in local government, very few authorities will be able to benefit from these changes.”