The UK’s leading doctors and public health experts have written to Boris Johnson, calling on the prime minister to act quickly to tackle poverty and end the gulf in life expectancy and health between the most affluent and the most deprived people.

Invoking his pledge to “level up” the new Tory constituencies that were once safe Labour seats, the leaders of 21 royal medical colleges and faculties point to evidence in the Marmot review published on Monday that the voters who brought Johnson to power live in worse health and will die sooner than his traditional supporters.

“We are sure you know that there is a 15-20 year difference in healthy life expectancy between some of the new seats represented by the Conservatives, and others that your party has traditionally held. These disparities directly impact on NHS services, with emergency attendances doubling in the areas of lowest life expectancy,” they write.

“From Redcar to Darlington, Barrow and Furness to Blackpool South we know that by the end of this parliament you will want to be able to demonstrate your commitment to your newly won seats. We urge you to focus the government’s efforts on extending healthy life expectancy and narrowing the life expectancy gap.”

The letter calls for the government to implement the recommendations of the Marmot review and improve the lives and prospects of people in deprived areas, investing in better childcare, education, housing, employment and incomes. The review by Sir Michael Marmot, the director of the Institute of Health Equity, found that life expectancy had stalled across England and that the gap in years of good health between the richest and the poorest – and between north and south – had widened over the last decade.

The letter specifically calls for improvements in incomes. “We know that earning a living wage is linked to healthy life expectancy. Poverty has most impact on infant and child health and focusing on this, as suggested by the report, is vital. While we are pleased that unemployment has fallen over the past 10 years, we are concerned that the number of people who are in work and claiming housing benefit has roughly doubled to a fifth,” it says.

“Your government should urgently consider increasing both the ‘national minimum wage’ and the ‘national living wage’ to be at least in line with the real living wage, as calculated by the Resolution Foundation. We know this would be a significant decision, but if not now then when?”

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Prof Maggie Rae, the president of the Faculty of Public Health and one of the signatories, said: “I just don’t think people understand poverty. People don’t understand in-work poverty. I think people have this mistaken historic impression it is because people won’t go out and work. But most of the people in these deprived communities are working, many of them in our much-needed public sector, including caring, policing and nursing.”

From their low incomes, people needed to pay for accommodation, often not cheap, as well as childcare. Some people would be on zero-hours contracts or in temporary jobs, which meant working people often slipped into poverty and debt.

Rae, who led the health inequalities unit at the Department of Health in the 2000s, said they had made progress on narrowing the gap in life expectancy between deprived and affluent communities before 2010. The government has the evidence for what works, she said. “This is a national scandal.

“This government says it wants to invest in the more deprived areas, so we have to work with them and get them to understand how they are going to do it now and be very clear that we have to improve life expectancy and narrow the gap.”