A survey from mortgage insurance providers Genworth found that 51% of MPs wanted private insurers to get ready to take over the risk of guaranteeing the scheme to relieve the taxpayer of this burden.

And the findings showed that 52% of those surveyed thought there was a risk that the scheme would become permanent.

Those who expressed concern about the impact the scheme would have on taxpayers if it were significantly called upon rose to 72%.

Angel Mas, president of Mortgage Insurance Europe at Genworth, said that while the influence of the scheme had been positive in bringing about competition at the high loan-to-value end of the market it was time to think about the future.

He said: “Just turning off the high LTV mortgage finance tap at the end of 2016 will risk a cliff since the issues that led to the introduction of Help to Buy 1 and 2 have not gone away.

“Access for first-time buyers to prudent high LTV mortgage finance will remain the lifeblood of a healthy mortgage market.”

Mas said that while there was optimism that the scheme would facilitate house building, a report from Morgan Stanley warned this could be damaged without long-term planning.

The report revealed house builders made investment decisions 12 to 18 months in advance which required a clear picture of what will happen to high LTV mortgage lending after 2016.

Mas added: “There is consensus that the scheme should not be permanent and over half of MPs see a potential role for the private insurance sector in replacing the government and minimising risk to the taxpayer.

“We believe that private involvement should be gradual and phased in through the life of the current Government scheme.”