Instead, the advisers said people should eventually replace boilers with heat pumps, which run on electricity and work a bit like a fridge in reverse: grabbing and compressing warmth from the outside air and using it to heat your home.
The upfront costs of a heat pump - and home upgrades needed alongside - are "sizeable" and price out poorer households, even with current government subsidies, campaigners and the CCC said.
While the first stage of the country's national climate action has "gone largely unnoticed", the next phase will be "a lot more difficult", said Adam Berman from Energy UK, which represents energy suppliers.
The two "most impactful" things households can do are replacing their car with an electric one and a gas boiler with a heat pump (only when they pack up, and not before), the advice said.
The committee's chief executive Emma Pinchbeck said: "Frankly, by the time a lot of people are going to be choosing a new car, the electric vehicle is just going to be the cheapest [option].".