Speaking on a weekly online show hosted by anti-capitalist platform Conter, Welsh said: “For the SNP I think they really do have to deliver a second referendum and they really did have the mandate after Brexit to do that.
“Now further down the line, patience will run out if they don’t deliver the second referendum.”
Welsh said it had been a major move to remove a country from a “whole set of European relationships”.
“People come up with and they use the numbers in the different voting systems … and a mandate for something down south isn’t a mandate in Scotland,” he added.
“It is nonsense, people have consistently voted SNP and they have voted for an independence referendum in this election.
“Really they should have gone straight to an independence referendum after the Brexit result.”
Welsh argued that most people in England “don’t care” about Scottish independence.
He added the “best English nationalist card” the Conservatives could play would be to say to Scotland and Wales to “just get on with it”.
On the issue of when another referendum might happen, Welsh said there would have to be some kind of deal between Nicola Sturgeon and Boris Johnson to break the impasse.
He added: “I think there is a big question mark over the political legitimacy of the British state now.
“When you look at what it has been for the last 40 years, it has been all about the distribution of resources of that state to a transnational elite and it seems to serve no other purpose.
“The way the SNP has managed to score is because it does have a defined project – it has a defined radical project which is independence.
“I think that decentralising project, that renewal project, is something in some ways going on right across these islands and I think it is to do with the secular decline of imperialism and deindustrialisation and the end of the UK as a state.”
Welsh was one of 1300 figures from the arts world in Scotland who signed an open letter supporting a Yes vote in 2014.
Writing about his reasons for backing independence in an article in the run-up to the vote, he argued getting rid of the “imperialist baggage” of the UK state will present new cultural and political opportunities.
He dismissed the notion it would lead to “conflict, hatred and distrust” between England and Scotland as the mindset of “opportunistic status-quo fearmongers” and “gloomy nationalist fantasists”.
“Swedes, Norwegians and Danes remain on amicable terms; they trade, co-operate and visit each other socially any time they like,” he wrote.
“They don’t need a pompous, blustering state called Scandinavia, informing them from Stockholm how wonderful they all are, but (kind of) only really meaning Sweden.”