The leaders of 11 of the UK’s leading food businesses have written an open letter calling for clearer rules on food labelling after the deaths of two Pret a Manger customers who suffered allergic reactions.

Pret is among the businesses that have signed the letter, which was first reported in The Guardian, organised by the foundation set up by the family of 15-year-old Londoner Natasha Ednan-Laperouse, who died after eating a baguette containing sesame seeds.

The businesses, which also include Greggs, Tesco, Sainsbury’s, Waitrose and Marks & Spencer, also want a mandatory system to ensure the swift reporting of food-related anaphylaxis cases.

Both issues were highlighted last year by the coroner hearing the inquest on Celia Marsh, a dental nurse from Wiltshire with a severe dairy allergy who died after eating a “vegan” Pret a Manger wrap contaminated with milk protein.

The senior coroner for Avon, Marie Voisin, said labels implying the absence of a particular allergen – especially terms like “free-from” and “vegan” – were “potentially misleading”.

The letter argues that the Food Standards Agency (FSA) needs to “make a clear decision on [allergen] thresholds and a strong recommendation to ministers.”

It continues: “This would provide sellers of food with an absolute definition of how much of a specific allergen pre-packed food could safely contain before being labelled as free of that allergen. Implementation would enable food producers to bring in consistent industry-standard testing and help keep the most allergic consumers safe and increase the choice of foods they can consume.”

The letter points out that Marsh’s death, like many other serious anaphylaxis attacks, was not immediately reported to the relevant authorities or even to the business that had sold the product.

It says: “This not only posed a risk to customers, but also impacted the investigation and learnings from Mrs Marsh’s death. Government and public health bodies must, as the coroner recommends, devise a “robust system” for the rapid reporting of fatal and near-fatal severe allergic reactions.”

The letter concludes: “We believe, taken together, these two actions could help save lives and build greater trust in the UK food industry for people with food allergies.”

In a statement, Marsh’s family welcomed the letter. They said: “These measures would make the world a safer place for allergy sufferers like our beloved mum and wife.”

Nadim Ednan-Laperouse, Natasha’s father and co-founder of Natasha’s Foundation, said: “We are delighted that the call for real change following Celia Marsh’s tragic and avoidable death is supported by many of the country’s biggest food businesses. It demonstrates that the industry shares our belief, and that of Celia’s family, that keeping their food allergic customers safe should be an absolute priority.

“It’s now over to ministers, health chiefs and the FSA to do the right thing by the 3 million people in this country living with food allergies and implement the coroner’s recommendations.”

The letter has been sent to No 10, the Department for Environment, Food and Rural Affairs, the health secretary, Steve Barclay, the Food Standards Agency, the UK Health Security Agency, the Royal College of Pathologists, the Royal College of Pathologists, UKHospitality and the Food & Drink Federation.

Michelle Victor, a partner at the law firm Leigh Day, who represents both families, said: “It is very good news that the UK’s leading food businesses have now come out in support of these measures.”