Inflation is expected to pick up to 0.4% when officials figures for June are published on Tuesday, as rising petrol prices and air fares push up the cost of living.
The Consumer Price Index (CPI) measure of inflation is predicted to step up from 0.3%, where it has remained for both April and May.
Economists will also be looking out for any impact from Britain's referendum on the European Union, although the data will come to early to factor in the plunge in the value of the pound following the Brexit vote.
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said: "The contribution of motor fuel prices to CPI inflation likely rose by about 0.4 percentage points in response to a 2.1% month-to-month rise in pump prices.
"A rebound in air fares inflation, following its surprise fall in May, likely also boosted the headline rate by a similar amount."
CPI was unchanged in May after transport costs climbed 0.9% after the price of diesel rose by 3p per litre in May this year, compared to 1.5p over the same period in 2015.
The cost of restaurants and hotels also rose, growing 0.5% in May compared with 0.2% the same month a year ago.
But these price rises were offset as food and drink prices edged down at the checkout, while c lothing and footwear prices eased back, down 0.2% between April and May.
Howard Archer, chief European and UK economist at IHS Markit, said CPI could even match March - when it reached its highest level since December 2014 - by hitting 0.5%.
He said: " Inflation is expected to have been primarily pushed up in June by higher petrol prices.
"Sterling's sharp plunge following the UK's vote to leave the EU on 23 June will have occurred too late to have had any impact on inflation in June, and it will likely take time to feed through.
"Nevertheless, the overall weakening of the pound from its late-2015 highs may have started to feed through to have some upward impact on inflation."
The CPI update comes amid a bleak outlook for the UK economy, with many economists slashing their growth forecasts and some pencilling in a potential recession following the Brexit vote.
The Bank of England held back from cutting interest rates from 0.5% this month, where they have remained since March 2009, but signalled action could be taken in August.
Investors and economists were taken by surprise , having expected the Bank to cut rates to 0.25% after Governor Mark Carney said in June that action would be taken over the summer.
Since then, the Bank's policymaker Martin Weale has questioned whether interest rates should even be slashed in August.
He said the Bank was "not a nurse to markets" and there were no signs that consumers or businesses were "panic-struck" following Britain's decision to leave the EU.
His comments came after economic data published on Friday showed UK construction output fell by more than expected in May, adding to concerns that the economy is in line for a sharp slowdown following the vote to quit the European Union.