The mortgages, once approved, would represent nearly £1bn of new lending to aspiring home owners.

Cameron hailed the success of the scheme which helps buyers who previously found the property market out-of-reach because of the size of deposit required.

David Cameron said: “Too many people have found themselves frozen out of the market in recent years as a result of the size of the deposit required.

“That is why as part of our long-term economic plan we introduced the Help to Buy scheme, so hardworking people with sufficient earnings can get on, fulfil their aspirations and enjoy the security of owning their own home.

“I want to see that continue in 2014 and for Help to Buy to help thousands more realise their dream of home ownership.”

In just 12 weeks since the scheme launched, nearly 750 homeowners have completed their purchases and hundreds were able to spend Christmas in their new homes.

Barclays and Santander will introduce Help to Buy products onto the market this month , joining Lloyds Banking Group, RBS, HSBC, Virgin Money and Aldermore.

The expansion will mean two-thirds of the entire UK mortgage market will offer products under the Help to Buy scheme, bringing home ownership to a growing number of people.

New figures also show that an additional 20,000 households have also been supported by the Help to Buy Equity Loan scheme, a separate scheme where the government provides an interest-free loan to support the purchase of the newly built home.

The large number of applications for Help to Buy mortgages suggests the high Loan-To-Value part of the mortgage market is once again moving.

High Loan-To-Value mortgages have been the main route to ownership for most first time buyers over the last 30 years, but there have been fewer products available in recent years.

House building is now growing at its fastest rate since 2008, and it is clear house building will remain a critical part of our economic recovery.