Charity Brain Tumour Research said the disease was the cancer most likely to kill patients under 40 in the UK.
They said charities made up more than 75% of the total national investment in brain tumour research, with the government funding sitting at 25%.
Following the announcement, chief executive Dan Knowles thanked Goodburn for his “tireless efforts” in raising awareness of the disease.
He said: “We are optimistic that this renewed focus will help ensure discoveries in the laboratory actually make it to patients who so desperately need more options.”
The Rare Cancers Bill, led by Edinburgh South West MP Scott Arthur, became law earlier this year.
The legislation aims to incentivise research and investment into the treatment of rare types of cancer, defined as those affecting fewer than 1 in every 2,000 people.
But Goodburn previously said that did not go far enough and a dedicated brain cancer lead would allow for greater focus on specific research and trials.
Arthur said the act was “vital” to driving research needed into the condition, but Goodburn’s meeting with Burnham could lead to further work in the field.
“There is real opportunity in the sector to dismantle the barriers to research that charities, clinicians, and researchers have known about for decades,” he said before the meeting.
“Having met Archie a number of times I know he is a fantastic advocate for the brain tumour community.
“I hope his meeting with the prime minister is a moment for concrete progress to be made.”