“What concerns me is that you can’t buy a house or a flat even if you are doing okay, you have got decent job prospects and good earnings.
“I am not prepared to be a Prime Minister of a country with caps on aspiration.”
The scheme aims to boost mortgage availability by reducing the risk for lenders because the Government takes on the risk of default when it guarantees a proportion of a loan.
It will see the state offer guarantees totalling up to £12 billion on £130 billion of high loan-to-value mortgage lending.
Mr Cameron believes that will help solve the skewed market that means people on good wages struggle to buy even modest properties because they cannot scrape together the massive deposits needed or find a mortgage.
Many properties are not available to potential buyers because they “don’t have rich parents”, he said on the eve of the Conservative party conference in Manchester.
A number of high profile figures have warned that it could lead to more problems than it solves.
Liberal Democrat Business Secretary Vince Cable warned the scheme “could inflate the market” and said he feared there was a “danger of getting into another housing bubble”.
Former Bank of England governor Lord King warned that the scheme is ”too close for comfort” to a general scheme to guarantee mortgages.
Mr Cameron dismissed concerns, telling The Sun people outside the M25 “laugh, quite rightly, in your face” at the suggestion there is a housing boom.
He said: “Look at the number of first time buyers – it is still almost half what it was before the difficulties that we faced.
“The number of mortgage approvals is still way below where it was.”
He added: “Don’t take it from me, take it from the Bank of England who looked at this last week and said there isn’t one”.
The first stage of Help to Buy was launched in April and offers loans to give people the chance to buy a new-build home with a deposit of just 5%. The scheme has been credited with spurring a surge in home sales and driving up prices.
Mr Cameron said tonight the “only one way you can improve people’s living standards” is to secure a recovery and “then you have got to cut people’s taxes”.
He told The Sunday Telegraph: “We do have to do more to explain how we are going to help people with the cost of living.”
Mr Cameron also insisted he was “not chasing off to the right” and was “very firmly anchored where I have always been”.
“Yes, I want to win back voters from Ukip,” he told the newspaper.
“But let me be clear, I am also a Prime Minister who is a modern compassionate Conservative who believes that there is a very important role for government in making sure that we look after the poorest in our society, that we are a compassionate society, that we give people opportunities who aren’t necessarily born with them. We are not going to abandon that.”
It comes as further revelations emerged from a book giving a glimpse into the heart of government, In It Together by Matthew d’Ancona.
The PM expressed private regret over pushing ahead with gay marriage reforms in the face of fierce opposition from many of his backbenchers, it claims.
The book says Mr Cameron told an ally: “If I’d known what it was going to be like, I wouldn’t have done it.”
Clashes between George Osborne and Iain Duncan Smith reportedly led to the Chancellor claiming the Work and Pensions Secretary is “not clever enough”.
Mr Duncan Smith, however, found Mr Cameron and Mr Osborne being in office comparable to “Ant and Dec” running the country, according to a friend.
Labour is enjoying a bounce in the polls at the expense of the Conservatives, according to a new study.
The YouGov poll for The Sunday Times puts Labour on 42%, the Tories on 31%, Ukip on 13% and the Liberal Democrats on nine points.
Shadow chancellor Ed Balls said: “If David Cameron is serious about helping first time buyers he should be bringing forward investment to build more affordable homes. Rising demand for housing must be matched with rising supply, but under this government housebuilding is at its lowest level since the 1920s.
“Unless David Cameron acts now to build more affordable homes, as Labour has urged, then soaring prices risk making it even harder for first time buyers to get on the housing ladder. You can’t deal with the cost of living crisis without building more homes, so it’s no wonder that for millions of families this is no recovery at all.
“The Bank of England should immediately review the details of the scheme now before they are set in stone, rather than wait a year. For instance, why has George Osborne decided that a scheme which should be about helping first time buyers will allow taxpayer backed mortgages for homes worth up to £600,000?”
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