The Office for National Statistics (ONS) said Consumer Prices Index (CPI) inflation rose to 9.4% in June, up from 9.1% in May.
This remains the highest level since February 1982 and heaps yet further cost pain on cash-strapped households and businesses.
Grant Fitzner, chief economist at the ONS, said: “Annual inflation again rose to stand at its highest rate for over 40 years.
“The increase was driven by rising fuel and food prices, these were only slightly offset by falling second-hand car prices.”
Newly appointed Chancellor Nadhim Zahawi and Bank of England governor Andrew Bailey have both pledged to get inflation under control.
Mr Zahawi said: “Countries around the world are battling higher prices and I know how difficult that is for people right here in the UK, so we are working alongside the Bank of England to bear down on inflation.”