* Cameron says agrees with BoE's Carney on housing risks
* Carney: Housing market poses domestic risk to recovery
* Cameron says would consider scaling back mortgage scheme
* Property prices soaring in London (Adds Lloyds tightening lending policy in London)
By Guy Faulconbridge
LONDON, May 20 Prime Minister David Cameron on Tuesday gave his strongest signal yet that Britain may need to cool its red-hot property market, saying he agreed with the Bank of England that the housing market was the biggest risk to financial stability.
House prices are soaring in London and have risen by a tenth over the past year in Britain as the economic recovery and record-low interest rates tempt purchasers back into one of the world's most expensive property markets.
But Bank of England Governor Mark Carney warned on Sunday that the housing market posed the biggest domestic risk to the financial stability of Britain's $2.5 trillion economy.
"I agree with everything he said in his interview," Cameron told BBC radio. "It is absolutely right that we are alert to any dangers and problems."
Cameron also said he would consider scaling back the government's 'Help to Buy' mortgage guarantee scheme if Carney advised such a step would be prudent.
Carney, who has repeatedly refused to be drawn on whether he sees signs of a property bubble in London, said the British housing market has "deep, deep" structural problems, chief among them insufficient construction of new homes.
Such stark warnings from Carney and now Prime Minister Cameron indicate a growing acceptance that something needs to be done to cool the market, especially in London where even some estate agents admit the soaring prices are unsustainable.
Hours after Cameron spoke, Lloyds Banking Group, Britain's biggest retail bank, said it was introducing tougher criteria on mortgage lending to help tackle rising prices in London's housing market.
The bank, which is 25 percent owned by the government, said it would limit mortgages to a maximum of four times a borrower's annual earnings when it is lending more than 500,000 pounds ($842,400) on a property.
The bank said the policy change will affect about 8 percent of its lending in London.
HOME OWNING DREAM?
Cameron's coalition government has faced calls from the opposition Labour party to scale back its 'Help to Buy' mortgage guarantee scheme which Cameron launched last year on the eve of the Conservative Party conference.
When asked if the government would consider changing the scheme to reduce its upper borrowing limit, Cameron said: "Of course. We will consider any changes that are proposed by Mark Carney."
'Help to Buy' allows people to buy property worth up to 600,000 pounds ($1.01 million) with deposits as low as 5 percent.
Carney said the BoE was checking the programme, which he said was targeted and relatively small though he cautioned it could grow a lot.
Cameron said the average property price bought under Help to Buy was 160,000 pounds and that 85 percent of the purchases were outside London and the south-east of England.
For Conservatives, 'Help to Buy' is the successor to Margaret Thatcher's 1980's 'Right to Buy' scheme which gave the residents of state-owned housing the right to buy their homes.
"Since the Second World War, Conservative leaders have always believed in a property owning democracy," Cameron said. "I have tried to relight the right to buy fire ... I want to see more people buy and own their homes."
The BoE's Financial Policy Committee, whose main task is to identify and remove risks to Britain's financial system, meets on June 17. ($1 = 0.5943 British Pounds) (Additional reporting by Belinda Goldsmith and Matt Scuffham; Editing by Andrew Heavens/Mark Heinrich)