He pinpointed “two critical points” which he said would put jobs at risk.
Mr Brown - the longest serving Chancellor of the Exchequer in modern times - said the impending double whammy would cost jobs.
He said the Chancellor, Rishi Sunak, would have to introduce further measures to limit the impact of rising unemployment, as his replacement for the costly furlough scheme was "very limited".
Addressing a Welsh Labour Party event, Mr Brown said: "I think we've got two cliff edges coming, if it is possible to go over two cliff edges at once.
"We've got October 31 and the end of the furlough scheme, and then we've got the end of the negotiations over Brexit.
"You've got two critical points where, at each of them, jobs are at risk."
Mr Brown went on: "There's not enough money available for furlough. His (Mr Sunak's) new proposals seem very limited.
"I believe the Chancellor will have to come back to the House of Commons quite soon to update, revise and change his plan, because it is simply not adequate for the circumstances of today.
"We praised him in March for doing the furlough, and I'm afraid now he has proved he is not doing enough to help us through this crisis. Unemployment will definitely rise very fast if he doesn't take further action."
Mr Brown was Prime Minister when a banking crisis hit the global economy in 2008. He said that international co-operation which was critical then is missing now.
"The G20 is not operational and there is no sense that there is a co-ordinated global strategy," he said.
"When you get a crisis like this - and this is a crisis worse than 2008 - you have got to be very clear what the problem is.
"It is clearly a health problem that's got to be dealt with and I can't understand why... Right at the beginning, when you have no vaccine, no cure and, therefore, no way of ending the disease, you have got to test, test and test.
"That's what we should have been doing right from the beginning, and the Government stopped testing in the first few weeks. I don't think we've ever fully recovered from that."
Mr Brown said there needed to be a strategy which was pursued with "relentless determination".
"I don't see that. What's happened is that the Government's reacted to day to day events, calls a press conference and deals with yesterday's problem," he said.
"But you've got to be two steps ahead.
"Everybody is suffering from the same virus, everybody is suffering from the same recession, everybody should know that you cannot cure this without every country having a cure for this, every country being able to wipe out the disease with a proper vaccine.
"Nobody is properly working together. You've got to bring people together.
"I fear the dynamism and the energy to do that is not there in the international community at the moment and it's very, very sad indeed, because we face the same problems."