The MMR jab should be compulsory for children before they are allowed to start primary school to stop the resurgence of measles and mumps, leading GPs are demanding.

Schools should ask all parents to prove their four- or five-year-old has had their two recommended doses of the vaccine before they can attend, they say in a letter to ministers seen by the Guardian.

They want school entry procedures toughened so that the only exceptions made to the new rule would be for children whose parents have registered a conscientious objection to the measles, mumps and rubella vaccine or those whose health means they cannot have it.

The four London GPs, who include a former government adviser on health policy, have urged the health secretary, Matt Hancock, and the education secretary, Gavin Williamson, to embrace the proposed change in policy. Doing so would save lives and tackle dangerous “complacency” among parents who do not ensure that their child is fully immunised, they say.

“Schools need to check that all their pupils have been vaccinated. In other countries, certificates of vaccination are required prior to school entry,” they say in the letter. “Here in the UK we could mandate that all children need to be vaccinated by a health professional, allowing for exemptions for either conscientious objection or medical contraindication.”

History shows that mandatory vaccination can be necessary, they add. “There is a precedent in the UK. Vaccination against smallpox was made compulsory for all children born after 1853 and today doctors need to show evidence of vaccination or immunity from various illnesses so we do not put patients at risk,” they say.

The four GPs include Sir Sam Everington, the chair of all the capital’s 32 NHS clinical commissioning groups (CCGs), which allocate health service cash in their areas. He helped advise the then health secretary Jeremy Hunt and was acting chair of the British Medical Association.

He is also the clinical (medical) chair of CCGs in north-east London while his co-signatories – Dr Mohini Parmar, Dr Andrew Parson and Dr Josephine Sauvage – occupy the same senior roles in the NHS in the north-west, south-east and north central regions of the city.

Their move comes as the proportion of five-year-olds in England receiving both doses has fallen in recent years to 87.2%, below the 95% the World Health Organization says is necessary to provide herd immunity and in effect eradicate measles, mumps and rubella. Public Health England figures show that cases of measles and mumps are rising sharply, a trend that doctors fear is linked to parents heeding misinformation spread by anti-vaccination campaigners.

Hancock recently refused to rule out a switch to mandatory MMR for primary schoolchildren and said anti-vaxxers had “blood on their hands”. “I do think we need to consider all options. I don’t want to reach the point of compulsory vaccination, but I will rule nothing out,” he said.

However, the GPs’ move triggered an immediate backlash. Medical and public health organisations voiced their unease and warned that making the switch would lead to “potential harms”.

Making MMR compulsory would be hasty, premature and “a kneejerk reaction” to falling immunisation rates, they said. Vaccination could deny patients a choice, lessen trust between patients and doctors and lead parents sceptical about the jab to home school their children, they warned.

Prof Helen Stokes-Lampard, the chair of the Royal College of GPs, said: “As GPs we have an important relationship with our patients, built on trust and understanding, and in order to keep that we need to help people make their own decisions. Positive, informed and educated choice is always going to be more desirable long-term, and we are concerned that rushing down the route of enforcing methods of healthcare could have unintended consequences.”

It would be wrong on principle to deny patients a choice over what medical interventions they had or to “impose” compulsory vaccination on them, she added.

“Mandation should be the end of the road, after we’ve tried everything else. There’s no body of evidence that it works. It’s a kneejerk reaction,” said Helen Bedford, the Royal College of Paediatrics and Child Health’s spokeswoman on immunisation.”

“If it’s linked to school entry, if you are opposed to vaccination then you are just going to go for home schooling,” added Bedford, a professor of children’s health at University College London.

The Royal Society for Public Health and Faculty of Public Health both opposed the plan.

Hancock declined to respond to the call. A spokesperson for the Department of Health and Social Care said: “We have a world-leading vaccination programme and uptake remains very high at around 90% for most childhood vaccines, including MMR.

“We are committed to driving up uptake rates further and our new vaccination strategy will draw together concerted efforts across the health system.”