The annual inflation rate as measured by the Consumer Prices Index fell to 2.4% in June, from 2.8% in May, the Office for National Statistics said.
The rate of inflation, which indicates how fast prices are rising compared with a year earlier, is slowing due to lower food, fuel and clothing prices.
The Retail Prices Index, which includes housing costs, fell to 2.8% from 3.1%.
This is the third month in a row that CPI has fallen.
The biggest contributor to the fall from May was clothing and footwear, which was 4.2% lower. This could be due to retailers starting their summer sales earlier, the ONS said.
The price of football shirts was “a notable exception” to this downward trend, it said.
The scale of the drop in clothing prices came as a surprise to some.
“We thought we would see some slightly more generous price discounting as the early summer sales kicked in, but nothing on this scale,” said Ross Walker, an economist at RBS.
Alcohol and transport costs were down by 0.5%.
Petrol prices fell by 4.3 pence per liter on the month, to £1.33 a liter on average. Diesel was down 4.7p to an average of £1.39.
Food prices were 0.1% lower. The biggest falls seen were in meat prices, the ONS said, with reports of weather affecting demand. This could be down to the wet weather leading people to cancel summer barbecues.
The slowing of the inflation rate brings it closer to the Bank of England’s target of 2%.
After such a long period of above-target inflation rates, the fall could mean that the Bank is more willing to inject extra money into the economy, through its stimulus programme known as quantitative easing (QE).
Earlier this month, the Bank said it would pump a further £50bn into the economy over the next four months through QE, taking the total size of the programme to £375bn.
Some members of the Monetary Policy Committee (MPC) have been concerned about the possible inflationary effects of extra stimulus.
“This will provide comfort to those in the MPC looking for further QE,” said Amit Kara from UBS.
“It might also reignite the debate on a policy rate cut, but in our view a rate cut is extremely unlikely, in the near term at least.”