Flights and fuel push everyday prices 0.5% higher
The average cost of everyday household goods and services went up by half a percent in June.
The UK inflation rate, as measured by the Consumer Prices Index (CPI), rose from 0.3% in May, official figures show.
The Office for National Statistics (ONS) attributed the rise to higher air fares, fuel and consumer spending.
Much of that was the result of European air travel, possibly connected to the Euro 2016 football tournament, it said.
The inflation figures are based on data collected before the EU referendum vote on 23 June.
The cost of plane flights jumped by a record 10.9% between May and June, ONS statistician Phil Gooding said.
"The growing cost of oil, feeding through to petrol prices, also helped to nudge up CPI," he added.
City analysts expect inflation to rise sharply in the coming months as the fall in the pound relative to other currencies following the Brexit vote makes goods imported into the UK more expensive.
The 0.5% annual increase in CPI matches that in March this year. It was last higher in November 2014.
But this measurement of the cost of living has remained well below the Bank of England's 2% target for more than two years.