Earlier this year, Ms Murray walked 200-miles from the site of her 29-year-old son’s death to London to campaign for Martyn’s Law.
“Certainly I feel this is the beginning of the end of the campaign, although there’s a bit to go still,” she said.
“I can see it’s coming to fruition now, finally.”
More than 100 public venues – from McDonald’s to the Slug & Lettuce chain – have signed a letter backing the bill.
John Shepherd, of the Manchester music venue, Band on the Wall, said: “Martyn’s Law will make people safer; that’s the bottom line and that’s why we are delighted to support Figen Murray and all those campaigning for change.”
Ms Murray told Radio 4’s Today programme it had been hard campaigning but “having your child’s ashes on a bookshelf is a good motivator”.
“I don’t want any other family member to be in this situation to have a relatives ashes on a bookshelf or have to visit a grave,” she added.
Additional reporting by PA Media.
