By William Schomberg and Stephen Addison

LONDON (Reuters) - Bank of England Governor Mark Carney gave his strongest warning to date about the risks of a housing bubble and said policymakers were looking at new measures to control mortgage lending.

The British housing market has "deep, deep" structural problems, 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 center in the housing market and that's why we are focused on that," he said.

British house prices rose about 10 percent in the 12 months to April but Carney has previously stressed that the BoE will seek to take measures to exert more control over mortgage lending before it resorts to raising interest rates, which could hurt the economic recovery.

Carney said on Sunday that the Bank would check lending procedures "so people can get mortgages if they can afford them but they won't if they can't".

He said 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.

"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," he said.

"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."

The BoE's Financial Policy Committee is due to meet in June to consider whether to introduce new measures to control the housing market.

Carney said the housing market in some areas of Britain was just starting to pick up but stressed the Bank was watching the recovery closely.

"What we're vigilant to, and we are vigilant about risk around the housing market, is to ensure that risks aren't building up for the medium term," he said.

"We don't want to build up another big debt overhang that is going to hurt individuals and is very much going to slow the economy in the medium term," he said.

"We'd be concerned if there was a rapid increase in high loan-to-value mortgages across the banks. We've seen that creeping up and it's something we're watching closely."

Earlier this month, the Organization for Economic Cooperation and Development called on Britain to take measures to help slow rising house prices, including a possible scaling back of the government's mortgage guarantee scheme, launched last year under its Help to Buy program.