The large-scale drive would also save the NHS £2bn and cut new cases of childhood asthma by 650,000, whilst also creating an economic and social boost for regions with the most inefficient housing, the charity said.
It said public and private investment in an "urgent" programme of retrofitting would tackle health inequalities, reduce household energy bills and help the UK reach its net-zero targets.
A study by the advisory service found that more than 15 million homes across Great Britain are energy-inefficient. It said 13 million of these could be upgraded to achieve a 'C' Energy Performance Certificate.
Its research also suggests that upgrading homes to EPC C level would prevent 570,000 children and adults developing mental health conditions associated with cold homes.
This would reduce the number of days of school and work missed due to illness and likely reduce the number of people kept out of work due to ongoing health conditions in the long term, it argued.
Citizens Advice chief executive Dame Clare Moriarty said: "The impact of raising minimum energy standards would be profound, giving a boost to household budgets, improving people's health, increasing energy security and helping the UK reach its net-zero targets.
"This report shows that insulating our homes is about so much more than reducing energy bills. It's a long-term solution that makes running the NHS cheaper and boosts quality of life in areas that need it most.
"The government must make improving our draughty homes a top priority."
In September last year, the Institute of Public Policy Research (IPPR) published a 28-year plan for insulating UK homes, which it said could save the country "billions". Proposals included retrofitting England's homes with good insulation and heat pumps, which would cut household bills and potentially create millions of jobs.
Earlier this year, the National Trust and Historic England were amongst a number of august institutions calling on the government to lay out a national plan to insulate the UK's historic buildings, including homes and commercial spaces.
Retrofitting the UK's historic buildings would support 290,000 jobs and boost the UK economy by £35bn as well as slashing Britain's carbon emissions, the 'Heritage and Carbon' report claimed.
For its part, the government announced a £1.5bn insulation scheme for low-income households in autumn 2022, in order to improve the energy efficiency of such homes. Through the 'Help to Heat' scheme, around 130,000 homes across England were estimated to be eligible to obtain external wall and loft insulation, energy-efficient doors and windows, heat pumps and solar panels.
