Banking sources said that the bank is considering implementing less stringent stress tests on new loans for more energy-efficient homes.

It is understood the bank has started small trials in its Halifax business, rewarding buyers of homes with an energy performance certificate (EPC) grade C or higher.

Owners of greener homes enjoy smaller energy bills that make their monthly mortgage payments more affordable. However, only 40% of the 22 million homes in England and Wales have an EPC rating of C and above and just 39,000 get the top A grade.

At the same time, just a tenth are rated B or above with ministers setting out their plans to decarbonise homes in the Heat and Buildings Strategy last year.

A source at Lloyds said that the bank is looking at how to tweak its offering to help mortgage holders retrofit their properties to boost energy efficiency.

A City source told The Sunday Telegraph: “There is a huge shift when it comes to mortgages and how lenders are looking at affordability. Because their homes are more efficient, their outgoings should be lower and lenders are considering taking that into account for affordability so it’ll just be a slightly better stress test.”

Another banking source added: “Everybody’s trying things at the moment because there’s no real experience of what buyers want or like.”