Lord Stuart Rose said customers are putting fewer items in their baskets and choosing from budget ranges more often as they try to mitigate price increases.
It comes as food price inflation hit a 13-year high on Tuesday, which means the average annual shopping bill is set to increase by £380 this year.
Lord Rose told the BBC that the supermarket is seeing “a massive change in behaviour”.
He said: “People are trading back. They are worried about spending. They’ve got a limit that they’ve set out, too. They say £30 is one limit… and if they get to more than £30 then that’s it, stop. It’s the same with petrol.”
Research from Kantar also found that shoppers are increasingly swapping branded items for cheaper, own-label products in an effort to stay within budget.
Sales of branded products fell by one per cent in the 12 weeks to 12 June, while own-label sales rose by 2.9 per cent and value own-label lines surged by 12 per cent.
Lord Rose called on the government to do more to help low-income households as the UK faces “some very tough times”.
“I’m of the generation that remembers what it was like last time,” he said, referring to the 1970s, when the Great Inflation hit and rates soared from 5.5 per cent in 1970 to 14.4 per cent by 1980.
“Once [inflation] gets hold, it’s quite pernicious,” Lord Rose added. “It takes a long time to eradicate… We’re in danger of being in a place that it’s very difficult to extricate ourselves from.
“What’s rather sad is that the country, the government, perhaps the Bank of England didn’t see inflation coming quickly. They’ve not recognised that.”
Data from Asda, which has been tracking disposable income since the financial crisis in 2008, shows that households had £40.38 less a week on average in discretionary income in May compared to the previous year.
The retailer added that half of its customers were worse off financially in May compared to 12 months ago due to mounting costs, which has the greatest impact on those aged under 30 and over 75.