The British public should take government predictions on the economic impact of leaving the European Union (EU) with a pinch of salt, the former Bank of England governor Mervyn King has warned, slamming the Treasury’s “simple minded” assessment of the risks.

Last week the Chancellor of the Exchequer presented a Treasury report to the House of Commons which made the claim that a British exit from the EU would leave every household £4,300 poorer a year.

But rebuking both sides for making finite economic claims, Lord King urged for the debate to be refocused on the wider picture, arguing that the reasons for either staying within or leaving the Union “cannot be reduced simply to the simple-minded level of a cost-benefit analysis.

“One should be very cautious of precise, numerical estimates of what the consequences would be,” he told Bloomberg TV.

His successor at the Bank of England, Mark Carney, has defended the Treasury report, telling the Lords Economic Affairs Committee that the findings are based on “sound” evidence. But Lord King appeared to contradict that, recalling that during the 1975 referendum on the same issue campaigners warned that it would make a dramatic difference. “It didn’t”, he said.

“I think it’s very important that people should not exaggerate the impact, either of staying in or of leaving,” he added.

“I do worry that proponents on both sides treating this as a public relations campaign rather than as a debate on the future of our country are inclined to exaggerate because they feel they are selling a position.

“What’s more important is that we have a calm and reflective debate about the role of Britain in Europe, our relationship with a continent which we have struggled with for several hundred years.”

Many pro-Brexit commentators have recently noted the use of almost apocalyptic language to warn against a Leave vote, such as the IMF warning that a British exit would cause “severe regional and global damage” to the economy.

But Lord King appeared to contradict this too, suggesting that the major threats to the European Union lie elsewhere.

“Europe as a whole faces two existential threats,” he said. “One is the Euro-area, where there problems are still fundamental and haven’t been solved. The second is the migration crisis. These are the big threats to Europe and hence to the world as a whole.”

Elsewhere, even supporters of the Remain campaign are starting to bemoan the government’s use of overblown rhetoric to make its case. Taking aim at the Chancellor’s dodgy £4,300 a year figure, the Spectator’s Fraser Nelson said it was “entirely false,” as it had been based on GDP, which doesn’t correspond to household income, and used Gordon Brown’s famous trick of dressing up a more modest increase as a cut.

“It’s not a fact, it’s an invention,” Nelson concludes. “If you assume that disposable income grows in line with GDP then he’d be arguing that there would be a £5,400 rise outside the EU by 2030 instead of £6,880 inside the EU – so the ‘cost’ of spurning EU membership would be £1,480.”

“Which could be alleviated with a modest tax cut.

“If he [Osborne] believed that leaving the European Union ‘would be the most extraordinary self-inflicted wound’ he might have told us – and his constituents – earlier, rather than proceeding with the farce of renegotiation.”