The former Prime Minister urged Scottish Labour to address the issues now and win back support for the party.
Appearing on Sky’s Trevor Phillips on Sunday show, Mr Brown was challenged on his party’s performance under new leader Anas Sarwar.
He said: “We’ve got to show that we’re both the party of social justice and that the Scottish National Party are not delivering that despite all their promises, and we are the party of solidarity.
“In this interdependent world, there is no future in nations that are neighbouring nations fighting each other and I fear 50 years of conflict between Scotland and England if we don’t get these problems sorted out.
“We’ve got to be the party of solidarity, talking about empathy, reciprocity, co-operation and sharing.
“Of course, we’ve found during the vaccination effort that when we co-operate we get things done.”
Mr Brown also urged the Prime Minister to consider his actions amid the ongoing issues around the Northern Ireland Protocol.
He said: “I think Boris Johnson has got to understand this is a union of England, Scotland, Wales and Northern Ireland.
“Each part of that union has got its own cultural traditions, its own sensitivities, its own needs and its own aspirations and you’ve got to work at this.
"The job of a prime minister is to unite the whole country, to bring people together.
“But you can’t assume the United Kingdom is going to hold together if you don’t work at it and that demands efforts, co-operation, policies for co-operation, instruments for co-operation and, of course, a determination that co-operation is going to work.
"I believe there should be a forum that brings together the nations and the regions in a more systematic way so that common problems are discussed, chaired by the prime minister.”
His comments came during an interview that also saw Mr Brown claim the G7 summit “will go down as a missed opportunity” due to the lack of a plan to deliver 11 billion vaccine doses.
He said: “When we needed 11 billion vaccines, we’ve only offered a plan for one billion.
“I think this summit will also go down as an unforgivable moral failure, when the richest countries are sitting around the table with the power to do something about it.
“Now that we’ve discovered the vaccine, we have not delivered the comprehensive plan that will deliver vaccination by the middle of next year.”
One of the topics discussed at the summit was helping the world recover, and Mr Brown warned the pandemic was hitting the poorest countries hardest and would widen inequality.
He said: “We will have a huge problem of a division between the richest countries that are safe and the poorest countries that are not safe.
“But then the problem will come back to haunt the richest countries because we will have contagion spreading that will hurt even the people who are vaccinated because of mutations and variants.”