David Cameron has criticised four Conservative grandees, including his former boss Norman Lamont, for questioning the independence of the Bank of England as infighting and jockeying for position at the top of the party intensified a week before the EU referendum.

Lord Lamont joined fellow former chancellor Nigel Lawson and ex-party leaders Iain Duncan Smith and Michael Howard to accuse the Bank and the Treasury of bias by warning about the economic consequences of a vote to leave the EU.

Writing in the Daily Telegraph, they said: “There has been startling dishonesty in the economic debate, with a woeful failure on the part of the Bank of England, the Treasury and other official sources to present a fair and balanced analysis.

“They have been peddling phoney forecasts and scare stories to back up the attempts of David Cameron and George Osborne to frighten the electorate into voting remain.”

Cameron, who was working for Lamont as a political adviser when Britain was forced out of the European exchange rate mechanism in 1992, expressed his alarm about the article.

He tweeted: “It’s deeply concerning that the leave campaign is criticising the independent Bank of England. We should listen to experts when they warn us of the dangers to our economy of leaving the European Union.”

Mark Carney, the governor of the Bank, has written to Bernard Jenkin, a senior figure in the leave campaign, accusing him of failing to understand the role of the Bank.

According to the BBC, in response to a complaint from Jenkin Carney wrote: “All of the public comments that I, or other Bank officials, have made regarding issues related to the referendum have been limited to factors that affect the Bank’s statutory responsibilities and have been entirely consistent with our remits.”

Lord Howard insisted it was wrong for the government to use the bank to support their campaign. He told Sky News: “I think it’s a great pity, frankly, that the government have tried to drag the Bank of England into this debate.

“It would have been much better if the Bank of England, which after all is going to have to work with a situation whatever it is after the vote, had stood aloof from the debate and remained completely impartial.”

The spat is the latest blue-on-blue row and comes a day after 65 pro-Brexit Tory MPs warned they would not back an “emergency budget” that Osborne had said was necessary if Britain voted to leave.

On Wednesday night, the home secretary, Theresa May – a likely leadership contender if Cameron resigns following next week’s vote – said she wanted further EU reform on immigration from Europe.

“There are some changes coming up in free-movement rules, to make it easier for us to deal with illegal immigrants, and I think again, as I’ve said, that we should look at further reform in the future,” May told the BBC.

The comments from May, who backs remain but has said little during the campaign, will increase pressure on the prime minister over immigration.

The leading leave campaigners Boris Johnson and Michael Gove wrote to Cameron asking him to “confirm whether it is government policy not to seek any further reforms of EU ‘free movement’ laws and regulations”.

But in her BBC interview May added: “What I’ve learned over six years is there’s no single answer … there’s no one thing you can do that can suddenly deal with all the problems and concerns over immigration and that includes leaving the EU – that’s not the single answer to this.”

The Financial Times, which has urged its readers to vote for Britain to remain, criticised Cameron for calling the referendum. In an editorial on Thursday, it said the vote had divided the country and caused a questioning of authority.

It stated: “David Cameron’s referendum gamble has proved to be a futile attempt to heal divisions in the ruling Conservative party. The campaign has split the country. Emotions have trumped facts. Born-again populists rail against the establishment.”

It added: “The positive case for Britain in the EU is easily made. To abandon the cause of constructive reform of an admittedly imperfect EU would be more than defeatist. It would be a gratuitous act of self-harm. Business leaders have a duty to spell out the cost of leaving before it is too late.”