Store price inflation rose to 4.4% in July from 3.1% in June, according to new figures.
The rise is the highest since the British Retail Consortium started its index in 2005.
Food inflation rose 7%, compared to 5.6% in June. This was partly due to an 8% increase in fresh food inflation, up from 6.2% in June.
Non-food inflation reached 3%, up from a record high of 1.9% in June, surpassing the previous record of 2.2% in April.
Helen Dickinson, chief executive of the British Retail Consortium, said: “Rising production costs, from the price of animal feed and fertilizer to the availability of produce, exacerbated by the war in Ukraine, along with exorbitant ground transportation costs, caused food prices to soar by 7%.
“Some of the biggest increases were seen in dairy products, such as lard, cooking fats and butter. Meanwhile, non-food prices were affected by higher shipping prices, costs of production and the continued disruption in China.
“As inflation reaches new highs, retailers are doing everything they can to absorb as much of these rising costs as possible and to seek efficiencies in their businesses and supply chain.
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“With households facing a cost of living crisis, retailers are expanding their value ranges to offer the widest variety of goods to those most in need, offering discounts to vulnerable groups and increasing staff pay.
“Nevertheless, households and businesses should prepare for a difficult period as inflationary pressures arrive.”
Mike Watkins, NielsenIQ’s Head of Retail and Business Insights, said: “Consumer family budgets are under increasing strain and price increases for food and non-food products have accelerated in recent weeks as increases of the prices of the costs are produced through the supply chains.
“The grocery industry in particular is under intense pressure as retailers try to protect customers from the full impact of inflation.
“At the same time, there has been an increase in competitive intensity, so retaining customers over the summer holiday season will be key in helping to stem a further drop in volumes.”