"What we'd love to see from government is a really serious, thought through, long term growth plan," he said.
"Long term growth is the only way in which we're actually going to be able to raise standards of living for our fellow citizens."
On Thursday Bank of England Governor Andrew Bailey said there was now more optimism about the prospects for inflation falling this year, prompting some lawmakers to call for early tax cuts.
But Allan, who is also chairman of housebuilder Barratt Developments and a former president of the Confederation of British Industry, said having a credible growth plan was much more important.
"There's nothing that is irretrievable about the UK economy, I'm an optimist in the long term, but in the short term I think we have some issues and those issues are having an impact on investment," he said.
British food inflation was 16.8% in December, official data showed on Wednesday.
Allan said Tesco's hope was that inflation would start to reduce around the middle of the year and would be somewhat lower by the year end.
"That doesn't mean prices are going to fall, it means that the increase in prices we hope will be much less sharp in the second half of this year, and it's probably going to be into 2024 and beyond before we see the normal level of inflation," he said.
"This year's going to continue to be very tough for many of our fellow citizens."
Last week Tesco reported better-than-expected Christmas trading.