The law on labelling allergens on food could be tightened as early as next summer, the parents of a teenager who died after eating a Pret a Manger sandwich have said after a meeting with Michael Gove.

The parents of Natasha Ednan-Laperouse said the environment secretary had told them he wanted a “Natasha’s law” to be introduced next year.

The 15-year-old, from Fulham, west London, collapsed on a British Airways flight from London to Nice on 17 July 2016 after eating a baguette that contained sesame seeds – an allergen not listed on the wrapper. She died later in hospital.

After meeting Gove, her father, Nadim Ednan-Laperouse, said: “I think we are moving to a tipping point, a really crucial point … a fundamental point for things to actually change in society, for people to become conscious in their conversations and their thoughts about allergies.

“So things that have previously been in the dark are now going to come out into the light. And that’s really really important, and only good will come from that.”

He said the positivity of the meeting with Gove had taken him and his wife by surprise. “That’s a wonderful thing for us, in our situation and also for all the other people who have allergies in this country,” he said.

After an inquest last month, Ednan-Laperouse said his daughter died because of “inadequate food labelling laws” and revealed he had promised the congregation at her funeral that she would receive justice.

The family have campaigned for greater consistency in labelling and want products to be labelled with complete allergen information.

Natasha’s mother, Tanya, told BBC Breakfast on Tuesday: “We taught Natasha to trust labels, to trust ingredients – she learned all the different words for different allergens.

“She could read a label and understand it by the time she was nine years old. It was very much a part of our life. There mustn’t be confusion with labels, it really does need to be standardised. If there is a label it should be the same everywhere.”

The pair said Gove told them a full review would be carried out between now and Christmas, followed by a consultation, and he could see no reason why the legislation could not be in place by the summer.

The Department for Environment, Food and Rural Affairs would be advising large companies such as Pret to change procedures before the law was introduced, Natasha’s mother said.

“He [Gove] felt it’s the right thing that they should be doing and they should start doing it as soon as possible because, he said, no one should ever, ever suffer a death such as Natasha’s that could be so easily avoided,” she said.

After the inquest, Pret a Manger agreed to full ingredient labelling on all products made in its shop kitchens.