More than £1.5bn of funding has been promised for West and South Yorkshire to build more social housing, the government has announced.

Amid questions over whether Labour can hit a target of 1.5m new homes by 2029, ministers have allocated West Yorkshire £1bn and South Yorkshire £700m under the previously announced Social and Affordable Homes Programme (SAHP).

Shadow housing secretary Sir James Cleverly said Labour had not revealed when the money to build the homes would be made available.

The Ministry of Housing, Communities and Local Government said the funding aimed to reduce the number of families stuck on waiting lists, with 180,000 social rent homes expected to be built in England.

The investment is part of the government’s previously announced 10-year affordable housing programme, which totals £39 billion.

The government said the funding pledge would “turbocharge social housing plans… and kickstart thousands of desperately needed new homes for local families”.

It said regional mayors would have the power to “shape the course of action” by setting out what type of homes will be built and where, though bids for funding would still have to be approved by Homes England.

Reacting to the news, Tracy Brabin, Mayor of West Yorkshire, said: “With council house waiting lists and private rents at breaking point, addressing the housing crisis is the most fundamental step our government could take to build a brighter Britain.”

South Yorkshire Mayor, Oliver Coppard, said the money meant everyone in the community could be offered “a high-quality home”.

In addition to social housing funding, a £150m package has also been allocated to mayors to fund the development of brownfield sites, with the aim of building 1,600 new homes across Yorkshire.

The government said £21m had been allocated for 841 homes in West Yorkshire, £12.3m for 492 homes in South Yorkshire and £7.3m for 292 homes in North Yorkshire.

Mayor of York and North Yorkshire, David Skaith said the money would enable more affordable homes to be built on brownfield land.

He added: “Our region is home to beautiful rural and coastal towns but, with rising rents, costs and second home ownership, working families are being priced out.”