* Carney points to lack of home building as big problem
* BoE to push banks on lending standards, consider new measures
* Bank considering merits of loan limits based on income - Carney
* Weak euro zone, stronger sterling are risks for economy (Adds quotes from Carney, Cameron, background)
By William Schomberg and Stephen Addison
LONDON, May 18 (Reuters) - Bank of England Governor Mark Carney gave his strongest warning to date about the risks of a housing bubble and said the BoE was looking at new measures to control mortgage lending amid a shortage of home building.
The British housing market has "deep, deep" structural problems, chief among them insufficient construction of new homes, Carney said in an interview with Sky News television broadcast on Sunday.
"When we look at domestic risk the biggest risk to financial stability, and therefore to the durability of the expansion, those risks centre in the housing market and that's why we are focused on that," he said.
Helped by a recovery in the economy, record-low interest rates and government schemes to help home buyers, British house prices jumped about 10 percent in the 12 months to April, raising concerns that buyers will take on too much debt.
Carney has previously said the BoE will seek to use its new powers over credit before it resorts to raising interest rates.
He made clear on Sunday that he saw the biggest problem in the property market as the shortage of new homes, saying twice as many houses were built each year in his native Canada than in Britain which has double the population.
Construction started on more new homes in England last year than at any point since 2007. But at 123,000 units, house-building remains short of the 200,000 which many economists consider to be the minimum needed each year.
"We're not going to build a single house at the Bank of England and we can't influence that," Carney said.
Also speaking to Sky News, Prime Minister David Cameron said Carney was "absolutely right" to point to the lack of housing but said government programmes were helping to get more built.
Britain has already toughened up checks for banks on mortgage applications and the BoE may take more measures as soon as next month.
The Bank was looking at the possibility of recommending that banks do more to limit the size of mortgages based on the incomes of borrowers, a potentially controversial move by the BoE that could be felt by many would-be homeowners, Carney said.
"The level of higher loan-to-income mortgages, ones above four and a half, five times loan-to-income, potentially could store up bigger problems for the future and we need to be careful."
"We need to be calibrated, we need to be proportionate, if we were to suggest some adjustments to the amount of these types of mortgages that banks should underwrite," he said.
He also said the Bank would be concerned if there was a rapid increase in high loan-to-value mortgages. "We've seen that creeping up and it's something we're watching closely."
The BoE's Financial Policy Committee meets on June 17. Other policymakers at the Bank have sounded increasingly concerned recently about the pace of the upturn in the housing market.
Earlier this month, the Organisation for Economic Cooperation and Development called on Britain to consider scaling back a state mortgage guarantee scheme launched last year by the government under its Help to Buy programme.
Carney said the BoE was checking the programme, which helps people get on the property ladder with only a small down payment, did not encourage risky lending by banks more broadly.
"It's a pretty targeted programme, it's a relatively small programme at this point but it could grow a lot and it could change attitudes in other parts of the mortgage market, that's why we have to be vigilant," Carney said.
"I would emphasise though that we do talk to the Treasury, I do talk to the Chancellor (finance minister), we try to be as co-ordinated as possible in ensuring that there is a sustainable development in the housing market and that's not in the short term, it's for the medium term."
Asked about other risks to Britain's economy, Carney mentioned weak demand in the euro zone and "persistent strength of the currency." He also said low levels of volatility in financial markets could pick up, pushing up borrowing costs.
(Additional reporting by William James; Editing by Bernard Orr and Rosalind Russell)