Mr Brown said: “This was a problem we expected with the flu vaccine if we had a no deal.
“Because so much of our medical equipment and our medical supplies actually do come from mainland Europe.
“Just like so much of our food comes from mainland Europe.
“So it’s really important that we don’t have a no deal.”
He continued: “It’s really important because if he doesn’t have a deal then he’s going to be at war with Europe and at war with America.
“President Biden has made it very clear that he won’t tolerate an American trade deal with Britain if we break the Good Friday Agreement.
“So there’s a lot at stake and I hope we can get an agreement soon.
“We really don’t want the chaos of not having a deal by Christmas.”
A number of vaccines around the world are now demonstrating promising developments.
The Prime Minister confirmed this month that the UK has ordered 40 million doses of the Pfizer vaccine.
US company Moderna also recently announced results from their preliminary trial data suggesting that their vaccine has an effectiveness of 94.5 percent.
Health Secretary Matt Hancock said that the UK has secured an initial agreement for five million doses of this vaccine to be available from spring 2021 should it be approved.
Additionally, the Oxford vaccine is reportedly showing “encouraging” immune responses in the over-60s.