The Chancellor told cabinet colleagues that while the London property market was recovering "relatively quickly", the property market in other regions had not enjoyed similar increases.
A government source told the MailOnline: "Vince and others should be out there making a virtue of the fact that we are the Government that has given the Bank that power."
Despite Osborne's insistence that house prices were only soaring in the capital, recent research by Hometrack found that house prices had increased by an average of 4.4% over 2013 in most parts of England and Wales.
Meanwhile property website Rightmove found that London house prices had soared by as much as £50,000 in a month.
Cable last week warned that the house price increases were increasing at a "worrying pace", adding: "The Government has done really good work turning the economy around: we can’t now risk it being derailed by a housing bubble repeating the mistakes of Gordon Brown."
The Bank of England has already moved to withdraw the Funding for Lending scheme which offered cheap credit to help mortgage lending, in order to focus on small business lending.
The government's Help to Buy mortgage guarantee scheme has sparked fears that it is helping push up house prices due to a continued lack of new housebuilding.
Cable urged the government last August to reconsider extending the scheme, saying: "We don't want a new housing bubble."
"I think in many parts of the country it clearly isn't a problem. If you are in Northern Ireland or Wales or indeed the East Midlands you would wonder what all this is about.
"But certainly in London and the south east, in the north east of Scotland, in other areas, there are serious housing inflationary pressures."