A ban on buy-one-get-one-free offers on junk food, as well as strict new rules on how and when it can be advertised, are among a host of measures aimed at tackling childhood obesity proposed by the leaders of the main opposition parties in a letter to the prime minister on Wednesday.

The letter, coordinated by the celebrity chef and healthy eating campaigner Jamie Oliver, also calls for action that would make healthier foods cheaper and easier to recognise, adding that the NHS is struggling to cope with the burgeoning obesity crisis.

“We don’t agree on everything, but we do agree on this: If we don’t act now, the current generation of young children could well live shorter lives than their parents,” the letter to Theresa May says.

It was signed by the Labour leader, Jeremy Corbyn, as well as the heads of the Scottish National party and the Liberal Democrats, Nicola Sturgeon and Vince Cable, and the joint leaders of the Green party, Caroline Lucas and Jonathan Bartley.

“We are writing to urge you to take bold action to tackle one of the greatest health challenges of our time. A crisis which is putting immense pressure on the NHS as it approaches its 70th birthday,” they write.

Saying a raft of measures needed to be introduced en masse to tackle the problem, they say they would support the prime minister if she banned multi-buy offers on junk food, stopped adverts for it before 9pm and online, and prohibited the use of popular cartoon characters and celebrities in ads.

Among other proposals, they call for the tax system to be “used to make healthy food cheaper and discourage unhealthy choices both at home and on our high streets”.

The leaders also say the levels of sugar, calories, salt and fat in junk food should be lowered overall, while more training should be given to medical staff to help people with nutrition.

A government source told the Times many of the opposition proposals were already in the pipeline as part of its anti-obesity drive.