Between June 2014 and June 2015, private rental prices paid by tenants across Britain increased by 2.5%, according to the Office for National Statistics (ONS).
This marks the strongest rate of year-on-year growth recorded by the ONS since January 2013.
The annual rate of growth in June would mean, for example, that a property which cost £500 a month to rent a year ago would now cost around £512.50 to rent if the cost had increased in line with the average uplift.
The annual increase is also well above the Consumer Price Index (CPI) measure of inflation, which slipped back to zero last month amid a run of falling food prices.
Private rental prices grew by 2.5% in England, 2.1% in Scotland and 0.8% in Wales in the 12 months to June 2015, the ONS said.
Rental prices increased in all the English regions over the year to June 2015, with rental prices increasing the most in London, which saw a 3.8% price hike.
Over the last year, rents have increased by 0.5% in the North East and the North West of England, by 0.7% in Yorkshire and the Humber, by 1.4% in the East Midlands, by 1.7% in the West Midlands, by 2.6% in the East of England, by 2.5% in the South East of England and by 1.8% in the South West of England.
The ONS's private rental index started in January 2011 - and since that time rental prices across Britain have increased by 10.2%.
Campbell Robb, chief executive of Shelter, said families paying "sky high" rents are being "left with no hope of a stable future".
He said: "O nly when politicians invest in building the genuinely affordable homes we so desperately need will they turn this crisis around once and for all."
The Money Advice Trust (MAT), the charity that runs National Debtline, also raised concerns about rising rents.
Jane Tully, head of insight and engagement at the MAT , said: "While many households will be able to shoulder these increases in housing costs as the economic recovery continues, we fear that rent arrears will continue to increase. At National Debtline we have seen the proportion of clients seek help with rent arrears double from 6% in 2007 to nearly 13% in 2014.
"With interest rate rises possibly only a few months away, we also expect to see additional pressure on private renters' budgets as landlords pass on these extra costs to their tenants.
"This means there has never been a better time for people who are renting to review their household finances - and seek free advice from a charity-run service like National Debtline if they are worried about how they will cope with increased costs."
Housing Minister Brandon Lewis said: "We're determined to create a bigger, better private rented sector that meets the needs of tenants and landlords alike.
"That's why we're attracting billions of pounds of investment in the market to build homes specifically for private rent, and have introduced a range of measures to ensure tenants know their rights and responsibilities.
"But we also want to ensure anyone who works hard and wants to own their own home has the opportunity to do so, which is why we've introduced schemes like Help to Buy so people can buy with a fraction of the deposit they would normally require."
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