Asda's monthly Income Tracker survey showed that the average UK family was £11 worse off each week during August and that the cost of living had risen 7.4% during the month.
Asda said that the average UK family had just £132 disposable income a week after tax and spending on essential items in August.
Spending on essential goods, which included rising food prices and rising energy bills, was up 5.5% over the month.
Asda chief executive Andy Bond said: "Food price inflation has peaked and with our latest price cuts we have thrown down the gauntlet to the rest of the industry to act. With Christmas looming, family budgets will be stretched and it is our job to help them make ends meet with long term price cuts."