Food and non-alcoholic beverage inflation fell by 0.2% month-to-month, with sugar, chocolate and confectionery seeing the largest drop in price.
Looking at inflation over the year, beef and veal price inflation eased from 9.4% in the 12 months to May to 5.1% in the year to June, while edible offal – which includes things like liver, kidneys and tongue – slowed from 9.2% to 3.4% over the same period.
Some other food items were cheaper, according to ONS data. Pizza and quiches, for example, fell by 6.7% in the year to June. Margarine dropped by 1.9% in the same period.
Food inflation often has a lag of up to 13 months due to the supply chain, so any effects from the war in Iran could still be yet to come.
Fuel prices at the pump fell in June after the US and Iran agreed to halt military operations and allow the key Strait of Hormuz to re-open.
But the recent resumption of hostilities and a new jump in crude oil prices means inflation could spike again in the coming months.
The British Retail Consortium (BRC) said lower food inflation was driven by “intense competition between supermarkets”.
“If retailers are to keep prices affordable for consumers in the long run, the Government needs to take practical steps to lower the everyday cost of doing business,” BRC economist Harvir Dhillon said.
“Andy Burnham has taken immediate action to ease pressure on household budgets; he must now look to do the same for businesses.”