Former Bank of England governor Lord Mervyn King has questioned the Treasury's analysis that leaving the EU could cost every UK household £4,300 a year, saying the issue "cannot be reduced simply to the simple-minded level of a cost-benefit analysis".
Mark Carney - Lord King's successor at the Bank - told members of the economic affairs committee at the House of Lords on Tuesday he believed the Treasury's report was based on a "sound" analytical process.
But Lord King told Bloomberg TV: "One should be very cautious of precise, numerical estimates of what the consequences would be."
He also accused both sides in the campaign of exaggerating and cautioned against expectations of a "dramatic difference" from either staying in the European Union or leaving.
He said: "I think it's very important that people should not exaggerate the impact, either of staying in or of leaving."
The former central bank boss called for 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".
He is the latest figure to wade into the row over the Treasury report, which claimed the UK economy would shrink by 6% by 2030 if Britain left the EU.
"I do worry that people 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," he said.
He added: "I'm old enough to remember the referendum in Britain in 1975 on exactly the same issue. The one thing that both sides of the argument then were wrong about was that it would make a dramatic difference. It didn't."
In his House of Lords appearance, Mr Carney repeated warnings that the economy is already beginning to suffer from the referendum uncertainty and said a Brexit vote could damage London's position as a key global financial centre.
He supported comments made last week by the Bank's Monetary Policy Committee that there had been "some softening in growth during the first half of 2016" due to uncertainty surrounding Britain's vote on the EU.
Mr Carney added it was "less likely" that London would be able to maintain its dominant financial position after Brexit.