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Karen Gray said she was "optimistic" after her MP, Lib Dem Christine Jardine, told her a meeting with UK Health Secretary Sajid Javid had given her confidence there would be "progress in the near future".
Ms Gray's son Murray was having hundreds of seizures every day until he started taking daily doses of the cannabis-based drug Bedrolite, but now the fits have stopped completely.
Ms Gray said: "He's fantastic – no seizures, he's at school full-time, it's just incredible."
But despite the legalisation of medicinal cannabis in the UK in 2018, Bedrolite is not licensed in this country and the Grays have to pay privately to obtain it.
Ms Jardine, MP for Edinburgh West, said her meeting with Mr Javid on Monday had been "much more positive" than her previous contacts with ministers from both the UK and Scottish governments on the issue.
She said: "He is looking for a way to break the logjam to allow the medical profession to feel confident in offering NHS prescriptions for patients with conditions like severe epilepsy.
"With Sajid Javid in charge I think there is a lot for affected families to take heart from."
She said her past representations to former UK Health Secretary Matt Hancock and former Scottish Health Secretary Jeane Freeman had left her feeling a lack of progress.
"But after speaking to Sajid Javid I came away from that meeting confident that he is aware of the need to make progress. He is after all the guy who made it legal when he was Home Secretary – and it hasn't developed in the way he anticipated.
"As Health Secretary he has other issues to deal with at the moment with Covid 19, but he said a lot of very positive things about his determination to enable GPs to prescribe on the NHS. I'm confident we will have progress in the near future."
Ms Jardine said the stumbling block so far seemed to be the fact Bedrolite was not licensed. "If it's licensed GPs can prescribe it on the NHS, but if it's not licensed then, as I understand it, there's no protection for them if something goes wrong.”
After speaking to Ms Jardine, Ms Gray, from East Craigs, said the situation sounded promising.
"I'm optimistic. When the law was changed in 2018 it was Sajid Javid that did it, so now he's the Health Secretary hopefully he can finish what he started and we will have access through the NHS.
"We've got to hope he will do something to sort out the situation and help everybody.”
Before a drug is licensed it has to be trialled and Ms Gray said she had recently had a meeting with the Scottish government when she was told the were keen to carry out trials, though nothing seemed to be happening yet.
She said: “Once they do trials I think they will see it really is beneficial because there are so many children and adults that are benefiting from it.”