This will mean the size of mortgage loans compared to a person's income or the value of the house could be limited if the Bank's Financial Policy Committee sees fit to use the new power, which will be introduced by the 2015 General Election.
If used, the same cap will also be applied to every Help To Buy mortgage under the UK Government scheme to aid first-time buyers get on the property ladder.
At present, there is a wide variation across the UK in terms of loans to income, with people in London getting mortgages about four times their salaries, in the rest of England it is about 3.5 times and in Scotland about three times.
Business Secretary Vince Cable yesterday said he was "appalled" that some banks had been lending five times a mortgage applicant's income, suggesting a "stable level" was up to 3.5 times.
Last night, in his annual Mansion House speech, George Osborne insisted: "I'm determined to back aspiration in every way I can, including the aspiration to own your own home.
"But I'm not going to opt for the easy route of some of my recent predecessors; duck the issues, risk a housing boom and keep my fingers crossed it won't damage the economy. So no irresponsible gambles with stability; no short-term fixes. Housing is a long-term problem and our economic plan will provide long-term answers."
The Chancellor said that while, at present, there was "no immediate cause for alarm", noting how house prices were still lower in real terms than they were in 2007, there was a need for vigilance.
"There are on the horizon things that should give us some causes for concern. If London prices were to continue growing at these rates (18% a year against 4% in Scotland) that would be too fast for comfort. And the rate of price rises is now beginning to spread beyond London."
While house prices in London are 25% above their 2008 peak, in Scotland only now are they reaching it.
During the last year, house prices across the UK have risen an average 11% and are close to pre-crisis levels. The International Monetary Fund last week urged the UK to take steps to cool the housing market and reduce the risk of a bubble.
Stressing he wanted the Bank of England to have all the weapons it needed to guard against a housing bubble, the Chancellor announced he was giving it new powers over mortgages, including over the size of loans as a share of family incomes or the value of the house.
"If the Bank of England thinks some borrowers are being offered excessive amounts of debt, they can limit the proportion of high loan to income mortgages each bank can lend or even ban all new lending above a specific loan to income ratio.
"And if they really think a dangerous housing bubble is developing, they will be able to impose similar caps on loan to value ratios; as they do in places like Hong Kong."
Shadow Chancellor Ed Balls said: "The fact George Osborne is consulting on new powers for the Financial Policy Committee, just a few weeks after he set out its remit, shows how behind the curve the Chancellor has been all along.
"The danger of his failure to act on housing supply is that we see a premature rise in interest rates to rein in the housing market, which ends up hitting millions of families and businesses."
He added: "You can't deal with the cost-of-living crisis and create a strong and balanced recovery without building more homes."