The father of a teenager with a dairy allergy who died after he unwittingly ate buttermilk at Byron burger has called on the company to do more.
Owen Carey ate grilled chicken at the O2 Arena Byron branch but the menu did not list the buttermilk marinade and he was not told about it on 22 April 2017.
Paul Carey said Byron still had to be persuaded to list allergens on menus.
Byron said it had enlarged its allergen notice on its menu and there was a reference to allergens on both sides.
Michelle Victor, from lawyers Leigh Day who represent the family of Owen Carey, said the law currently gives discretion to food businesses to provide allergy information in writing or orally.
But she said under Owen's Law, which the family have called for, businesses would be required to provide allergen information on the menu and staff would also be required to ask diners if they have any allergies. This would provide more transparency to those with allergies about what's in their food and provide more protection than the law as it currently stands.
Mr Carey said Byron had accepted waiters should ask customers about allergies, but said it was "not enough".
He said: "The key element of Owen's Law is this matter of putting the allergens on the face of the menu and I don't know yet whether we can persuade Byron that it is an easy thing to do."
Mr Carey added: "It may be inconvenient, but it's not difficult. It's not impossible to put symbols of some kind."
Simon Wilkinson, Byron chief executive, said the company was keen to work with the family and government to improve signposts without losing "key interaction and discussion between the guest and staff to ensure their allergies are shared also with the kitchen".
He said staff had been asking customers if they have allergies for 18 months, the till system had an on-screen reminder for staff, allergy information was recorded on receipts and staff had to verbally alert the kitchen team about customers' allergies so food was prepared accordingly.
The allergy message on the menu now took up a third a page, he added.
Mr Wilkinson said there were flyers on tables reminding customers to inform staff of allergies and all Byron restaurants had an "allergy champion".
After Owen's inquest, assistant coroner Briony Ballard warned a failure to draw together lessons from food allergy deaths was contributing to the number of fatalities.
The teenager, from Crowborough, Sussex, died as he celebrated his 18th birthday in Greenwich with family and friends.
After he collapsed outside the London Eye, members of the public tried to revive him but he later died.