Despite prime minister David Cameron again making a case for the Help to Buy scheme at the Conservative Party conference in Manchester, only two banks have so far committed to supporting it.

Both of them – Lloyds Banking Group and Royal Bank of Scotland – are themselves two banks which had to be propped up with government money during the financial crisis.

The second phase of Help to Buy will aid people buying a home for the first time as well as homeowners who already have a foothold in the housing market – with both groups eligible if the property is worth £600,000 or less.

A five per cent deposit is needed, while the lender will buy a government guarantee which will be used to cover anything up to 15 per cent of the value of the property.

However head of mortgages at the Building Societies’ Association Paul Broadhead told the Telegraph that about a third of building societies already offer mortgages which are underpinned by private insurance companies – so they are unlikely to join the Help to Buy scheme as it will be “too much effort to switch”.