Celia Marsh died after eating the super veg rainbow flatbread while shopping with her family in Bath in 2017.
The coconut yoghurt dressing had been cross-contaminated with milk protein during manufacture, the coroner said.
The inquest was told Marsh, 42, 'religiously avoided' dairy after a near-fatal experience months prior.
She was declared dead less than two hours after eating the wrap, having collapsed in the street.
Maria Voisin, senior coroner for Avon, reached a narrative conclusion following a two-week inquest, held at Ashton Court in Bristol.
One of Mrs Marsh’s daughters, Ashleigh Grice, said her mother had lived in 'constant fear' and checked every food label to see if it contained dairy, 'often triple checking'.
“Mum’s death, like so many other allergy deaths, was entirely avoidable,” she said.
Ms Voison said Mrs Marsh had suffered an anaphylactic shock after eating the wrap.
“A product which is marked dairy free should be, free from dairy,” the coroner concluded.
The family welcomed recommendations made by the coroner which include bringing in compulsory testing for products claiming to be dairy and allergen free.
The protein was in an ingredient called Coyo that contained an extra ingredient called HG1.
“The contamination arose because the ingredient HG1 was cross-contaminated during manufacture,” said Ms Voisin.
“The manufacturer of the dairy-free yoghurt had in its possession documents which flagged this risk, but this risk was not passed on to its customers,” the coroner ruled.
Mr Marsh’s family gave a statement outside the inquest, calling for tighter rules on food production
The coconut yoghurt used as dressing came from Australian brand CoYo, and was licensed for manufacture in the UK to British firm Planet Coconut.
The CEO of Pret a Manger, Pano Christou, said the company 'fully supported' the coroner’s findings.
“As a father and husband, I can only imagine how distressing this has been for Celia’s children and family,” he said.
“Our deepest sympathies remain with everyone who knew and loved Celia.
“As the Coroner made clear, Planet Coconut had information which should have alerted them that their Coyo yoghurt may have contained milk and this information was not passed on to Pret.
“It goes without saying that if Pret had ever known that the Coyo yoghurt may have contained milk, we would have never used the ingredient.”
Christou added that his company had taken 'significant steps' involving its suppliers and labelling policies since Mrs Marsh’s death to ensure all customers were informed about the food they were buying.