The bodies believe that this must happen in order to provide greater protection for consumers.
In a letter to the Economic Secretary to the Treasury, Kitty Ussher, the organisations expressed concern that some of the schemes may not be treating consumers in a fair manner.
Concerns about sale-and-leaseback schemes include the fact that many offer very little security of tenure, and properties are often purchased at a discounted rate without an independent valuation. Some schemes have been criticised for the way in which they treat consumers at a potentially vulnerable time when they may be facing repossession.
The group also believes there is good case for advertising, sales and customer care standards to be investigated by the Office of Fair Trading. A lack of understanding about the products by consumers and the potentially misleading way in which some schemes are advertised has created confusion and potential detriment for some consumers in an unregulated marketplace.
Michael Coogan, CML director general commented: "Controls exist for action taken by mortgage lenders when customers are in arrears but there are no such safeguards for customers entering into sale-and-leaseback schemes.
"In a climate of rising repossession, consumers in financial difficulty need to be well informed and protected. The government needs to consider urgently whether regulation of sale-and-leaseback schemes by the Financial Services Authority is appropriate because it would provide protection for potentially vulnerable consumers."
Teresa Perchard, Citizens Advice public policy director, said: "This is a growing problem and a completely unregulated sector which we think the government needs to look at. We have seen a number of cases where people in mortgage arrears and facing the threat of repossession have gone ahead with a so-called 'mortgage rescue' scheme on the understanding this would allow them remain in their home in the longer term, only to find themselves homeless within a year.
"These schemes can be difficult to understand, and the information about them can be misleading. Usually people will be required to sell their home at much less than its market value and they will have very little security of tenure as a tenant, but this is not always made clear.
"Mortgage lenders have a duty to treat borrowers in trouble sympathetically and fairly, so we would we would urge anyone with mortgage arrears to first talk to their lender, and to seek free, independent advice as quickly as possible."
Adam Sampson, chief executive of Shelter, said: "The actions of some companies offering 'sale-and-lease back' schemes amounts to daylight robbery, leaving growing numbers of people financially ruined and homeless.
"The Government must urgently introduce regulation to stamp out this unscrupulous practice, which is cashing in on people's financial problems and deepening their misery."