Mortgages are set to rocket by nearly £1,000 a year if Britain quits the European Union, David Cameron has warned.

Short-term uncertainty caused by a vote in favour of leaving the 28-member block would tighter credit conditions and fuel a rise in interest rates, according to Treasury analysis.

But the Leave campaign claimed that voters "cannot trust" Government on the EU.

In a robust letter to the Prime Minister and Chancellor, Boris Johnson and Michael Gove warned that remaining leaves the country "dangerously and permanently exposed to being forced to hand over more money and accept damaging new laws".

Remain campaigners dismissed the letter as "reckless nonsense" and accused the Brexit camp of "misleading" the public.

Stronger In said the average new mortgage will cost £920 a year while first time buyers, who generally have lower value loans, face paying £810 more annually.

"Nearly all experts agree there will instant shocks to the economy if we leave the EU and there is a clear and present danger of higher mortgage rates," the Prime Minister told The Mail On Sunday.

Combined with predicted higher unemployment and lower wages following a Brexit, the hike in mortgages would make it much tougher for first time buyers to get onto the housing ladder, they warned.

But Mr Johnson, the Justice Secretary and Labour's Gisela Stuart branded Treasury analysis previously released by the government predicting Brexit would hit households by more than £4,000 as "indefensible" and "bogus".

Setting out detailed claims about the "dangers" of the EU, they criticised the Prime Minister's renegotiation package for failing to secure real change.

Britain will be forced to bow to the will of eurozone nations if it remains in the bloc and will be pushed into funding future bailouts for ailing members states, they warned.

"If we stay, we are tying ourselves to a broken Eurozone economy while simultaneously accepting unlimited migration of people trying to escape that broken economy," they wrote.

"British taxpayers are already paying nearly £2 billion for Albania, Macedonia, Montenegro, Serbia and Turkey to join the EU. The European Commission recently announced an acceleration of these plans and is already extending visa-free travel to the border with Syria and Iraq. This is dangerous. The Government's claim that Britain has a veto is meaningless if it is simultaneously trying to 'accelerate' this process."

Jayne-Anne Gadhia, chief executive of Virgin Money, said: "Even if the base rate stays flat after a vote to leave the EU, mortgage prices could rise considerably - leading to more expensive monthly mortgage payments for everyone."

A Britain Stronger In Europe spokesman said: "As any credible expert will tell you, this letter from Leave is reckless nonsense - they are now guilty of actively misleading the British people.

"The Leave campaign cannot produce a single expert who believes there is any prospect of Turkey joining the EU. The UK retains a full veto over any new member.

"We have clear guarantees we will not contribute to bail outs and protections against Eurozone integration."

George Osborne weighed in on the economic arguments for a Remain vote by claiming first-time buyers, some of whom have been encouraged by the thought of lower house prices, would also suffer.

In an interview with The Sunday Times he said any gains would be offset by rising mortgage costs and people were not helped on to the housing ladder by "crashing the economy".

Mr Osborne said: "If we quit the EU the country would be poorer, there would be volatility in the financial markets and that would push up mortgage costs irrespective of what the Bank of England might do with official interest rates."

He also described the referendum as a "battle for the soul of the country" and slammed the leaders of the Leave campaign as "conspiracy theorists".

"This is a battle between Farage's mean vision of Britain and the outward-facing, generous Britain that the mainstream of this country celebrates," he said.

"I say: we don't want Farage's Britain. That means voting to remain."

Michael Gove, also speaking to The Sunday Times, hit back at the comments saying that claims by the Prime Minister and the Chancellor that Britons would not be forced to bfund another EU bailout were dishonest."

"In the past we've been assured that we would not be on the hook for bailouts," he said.

"And yet when crises have hit, the EU has broken its own rules in order to provide bailouts and has forced Britain to pay."

But the Justice Secretary seemed to step back from all-out war on his Conservative Party colleagues by saying he knew that "there is no one who will fight better against this than George".

Fellow Brexit campaigner Iain Duncan Smith said a vote to Remain would lead to the UK becoming part of a "single federation in he eurozone" and outlined what he described as the "risks" of the scenario.

The former Cabinet minister argued for Australian-style points-based system to manage immigration if the UK votes to leave.

Writing in The Mail on Sunday, he said: "We can remain inside an undemocratic, dysfunctional EU that is headed towards a supranational government which will take away more powers from democratic nation states while permitting mass migration.

Alternatively, we can stay friends and keep trading with Europe and the rest of the world - while retaking control of our government and our borders."