The consumer price index (CPI) measure of inflation shows prices are still rising, just at a slower pace than before, as the rate fell from 8.7% in the year to May.
Another measure of inflation, closely watched by the Bank of England when deciding whether to increase interest rates, also fell.
Core inflation – the rate of price rises that excludes food and fuel – dropped to 6.9%. The rate had been increasing since January this year.
Most analysts now expect that the Bank will only increase the base interest rate to 5.25% early next month. Prior to the inflation announcement, an increase to 5.5% was seen as the most likely outcome.