Burton-Sampson said: “There’s some progress being made now in trying to get Biogen in front of the right people at the Department of Health and Social Care, including the minister.”
He said accelerating the discussions was crucial so people like Brogan could “live a better life”.
“We are doing everything in our power to try and make that difference and we’ll continue to do so,” Burton-Sampson pledged.
“There’s a drug out there that could slow this down, and the fact she currently doesn’t have access to this drug is really, really tragic.”
Brogan and her family delivered a letter to 10 Downing Street on Tuesday, pleading with the prime minister for help.
It followed a petition on the matter attracting 100,000 signatures, including from ex-heavyweight champion boxer Frank Bruno.
Brogan said of the drug: “It will be a massive deal, just having that little bit of hope that I can be cured one day and I can live a normal life.
“It’s just awful, I wouldn’t wish this on any other teenager.”