Fears have been raised that the attempt to kick-start the market could result in a house price ''bubble'', with the market overheating and borrowers over-stretching themselves.
This is of particular concern in London where prices have risen by around 10% year-on-year.
From January the Help to Buy initiative will provide mortgage guarantees on properties worth up to £600,000 but the Bank's Financial Policy Committee (FPC) will make annual reviews and could recommend that the cap is reduced.
It was initially due to only assess the scheme after three years.
The FPC could also make loans more expensive by recommending that the Treasury raises the fees paid by lenders for the guarantees.
Business Secretary Vince Cable has voiced concerns that the scheme could lead to an asset price bubble.
But Mr Osborne said last week " let's not pretend there's a housing boom" and insisted it was important to "go on trying to fix specific problems in our financial system".
"The FPC's assessment this week - in line with that of the Chancellor and the Governor - is that recent developments in the housing market represent a broadening recovery from low levels of activity, but that we must remain vigilant as that recovery progresses.
"The Chancellor has asked the FPC to work with him every September, starting next year, to assess the ongoing impact of the Help to Buy scheme. Following that annual assessment he has proposed that the FPC advise him on whether the key parameters of the scheme - the price cap and the fees charged to lenders - remain appropriate.
"At the end of the scheme's three-year life, if a future government proposes to extend the scheme, the FPC will have to give its agreement."