A new £3bn scheme will fund the building of 30,000 affordable homes, the chancellor has said, as he proclaimed that the government was on track to reach its target of 300,000 new homes a year in Britain.

Philip Hammond’s spring statement also contained a patchwork of separate schemes to boost housebuilding, including £717m to “unlock up to 37,000 homes” in the Oxford-Cambridge arc, Cheshire and west London.

“The government is determined to fix the broken housing market,” said Hammond. “Building more homes in the right places is critical to unlocking productivity growth and makes housing more affordable.”

Under the affordable homes guarantee scheme – an existing programme that will receive renewed government support – the government does not directly fund new homes but gives a Treasury guarantee to housing associations to allow them to build.

The housing charity Shelter said while it welcomed the boost for affordable homes, borrowing by housing associations would not solve the housing crisis, and the government needed to fund much higher levels of social housing.

Polly Neate, chief executive of Shelter, said: “The government’s decision to renew the affordable housing guarantee scheme is a welcome announcement. This initiative will support the building of more desperately needed social and affordable homes.

“While this is good news, it has to be noted that we can’t deliver social housing on the scale we need on borrowing alone – 3.1m social homes are needed in the next 20 years to tackle the housing crisis at its root and lift thousands of families out of homelessness. We need much more grant funding for social housing in this year’s spending review to get a grip on our ever-growing housing emergency.”

Official government figures show that affordable homes – for sale or to rent – make up a relatively small, but growing, part of the housing supply in England.

In the six months to 30 September 2018, there were 9,909 new affordable homes started, up from 6,989 in the same period of 2017.

The definition of what “affordable” means is controversial. The government defines it as “social rented, affordable rented and intermediate housing, provided to eligible households whose needs are not met by the market”. It includes shared ownership homes for sale “provided at a cost above social rent, but below market levels”.

But some shared ownership homes come at eye-watering prices. Currently a shared ownership two-bed flat in London is on sale for £985,000 at full market value, with the buyer taking a 25% share and expected to find £2,469 a month in mortgage and rent repayments.

In recent weeks reports have suggested that some housing associations in the London area have been left with hundreds of unsold shared ownership properties.