Chancellor Philip Hammond said the mortgage guarantee element of the Help to Buy scheme will close at the end of 2016 as planned.

The government-backed guarantee was available for lenders to underwrite new repayment mortgages on homes up to a value of £600,000. The mortgage had to be 4.5 times or below the borrower's income.

It was intended to reduce mortgage costs for people buying homes at a high loan-to-value ratio as house prices rose well ahead of incomes, fuelled by a protracted housing shortage.

In a letter to the Bank of England governor Mark Carney, Hammond said over 86,000 households had been supported by the Help to Buy mortgage guarantee. The average property price in those purchases was £157,000, he said, well below the national average of £217,000.

"Moreover, the high LTV mortgage market has become less reliant on the scheme as confidence has returned," the chancellor wrote.

"There are now over 30 lenders offering 90-95% loans outside of the scheme. This reflects the fact that the scheme was introduced with a specific purpose that has now been successfully achieved and, as such, I can confirm that it will close to new loans at the end of 2016 as planned."

When unveiled in 2013 by George Osborne, the previous chancellor, critics said the government was reckless in guaranteeing mortgages because it put taxpayer cash at unnecessary risk and would fuel house price growth further by inflating demand when there is a dearth in supply.

But in his letter, Hammond said he was "pleased to note the [Financial Policy] Committee's conclusion that the scheme has not posed material risks to financial stability in the UK and has not been a material driver of house price growth."

The equity loan and ISA parts of the Help to Buy scheme remain in place.