The governor of the Bank of England, Mervyn King, has privately warned Downing Street that he will resign if Gordon Brown directs the bank to become the key agency in a state-backed mortgage guarantee system.

Transferring the risk of investing in mortgage-backed bonds from investors to the Treasury, a move that would see the government "underwriting" mortgage deals, is understood to be one of the key recommendations contained in the final report from Sir James Crosby, the former head of HBoS. Crosby was commissioned to look at new ways of reviving the UK's ailing mortgage market.

Sources say the Prime Minister believes a temporary guarantee system, with the government refinancing bonds every two or three years, could be the magic bullet that revives the housing market and Labour's political fortunes.

Crosby's full report - expected to be published before Alistair Darling gives his autumn pre-Budget assessment on Britain's economy - is already with the Chancellor. Despite Crosby backing state "under-writing" of mortgages, but backing away from a full-blown introduction of a UK version of the US Fanny Mae/Freddie Mack model, Treasury economists privately attacked the proposal as "unworkable" and "liable to prolong" the credit crunch. Darling is understood to have told Number 10 that such mortgages would be a burden that the government should not bring upon itself.

King told the parliamentary Treasury select committee last week what he has repeatedly been telling financial institutions: that any attempt to artificially support the mortgage market by the government is something a central bank should not be doing.

In private, King has let Number 10 know that he believes risk and reward is part of the market and underwriting mortgages is not something in which the Bank of England should do.

With Darling opposed to the introduction of state-backed mortgage guarantees, with his stance backed by King and leading figures at the Bank of England, the replacement of Darling in the expected Cabinet reshuffle will set alarms bells off in Threadneedle Street.

One Bank of England source said: "The governor has made his position crystal clear. It is not the purpose, nor should it be, of central bank liquidity insurance to provide a source of long-term funding to the financial system." Asked whether or not Number 10 knew that King's opposition amounts to a serious resignation threat, the source said: "Yes, they know and understand that."

Given the pressure that the Prime Minister is under to show his party and the country that he has a solution to get Britain out of the economic downturn, the resignation of King would be, according to one Treasury aide, "an economic catastrophe". He added: "The government's credibility would be shattered, leaving Brown and perhaps the new Chancellor in an economic no- man's land."

Equally worrying for Brown is that political dithering over the Crosby recommendations will not be welcomed by agencies at the centre of the housing crisis, such as the Home Builders' Federation (HBF).

The HBF says that the housing crisis is well advanced and that if there is no urgent action by the Treasury to improve market conditions then further damage to the economy can be expected.