Paul Johnson, director of the Institute for Fiscal Studies, also said struggling public services will need more investment after the Bank of England predicted the UK would be plunged into the longest slump since 2008.
Sources in the Liz Truss camp did not deny that her planned emergency budget could come as early as September 21, as the dire state of the economy becomes the main issue in the race for Downing Street.
But Mr Johnson was scathing about the state of the debate so far.
Why the Tory leadership candidates remain so focused on tax "remains a mystery," he told BBC Radio 4’s Today programme.
He also called on candidates to stop talking about the fiscal ‘headroom’ announced back in March.
“With the economy changing and completely going into recession, inflation much higher than expected, those numbers are massively out of date,” he said.
"What they need to be talking about is how they think they’re going to be tackling inflation, how they think they’re going to be responding to the increased needs of households and how they’re going to be responding to what this means for public services, and it remains a mystery to me why they’re so focused on tax."
He said there would have to be more money for public services and the next prime minister would “have to find many more billions to support households” to pay rising energy bills.
Mr Sunak has accused Mr Truss of planning tax cuts that are inflationary, warning that her proposals risk pouring “fuel on the fire”.
Truss supporter and business secretary Kwasi Kwarteng told Sky News that the tax plans favoured by Rishi Sunak are “perverse”.
He said he “never understood how we are going to help people, by putting up their taxes”.
He also said the mandate of the BoE would be reviewed if she wins the election.
“We need to look again at what their mandate is,” he said, “if your target is 2 per cent and you are forecasting 13 per cent something has gone wrong”.
He also defended the chancellor and the prime minister, both of whom are understood to be on holiday.
He added: "I’m the business secretary, I’m here in a suit, I’m not on holiday.”
The governor of the Bank of England Andrew Bailey rejected the criticism that it should have raised interest rates earlier. He said the bank had been increasing rates since December and that rocketing inflation is what "concerns me most".
He also warned that workers unable to secure wage increases could suffer more if some sectors saw large pay rises.