Rent increased across England and Wales by 3.5% in the year to May 2013, taking the average rent to £737 a month.
This was the third highest level on record, according to LSL Property Services, which said rents rose by 0.1% between April and May.
Tenants in the capital experienced the largest annual increase, with rents rocketing by 7.2% in London; while tenants in Wales experienced a 5.2% increase and those in the north east of England a 4% rise.
The only one of the ten regions not to post an increase in the last year is the south west of England, which was unchanged on a year ago.
LSL said that the 0.1% rise in May could have been much higher had it not been for a recovery in the housing market in recent months.
The Council of Mortgage Lenders announced that in May 2013 mortgage lending jumped to its highest monthly level since October 2008 – up 21% on April and 17% higher than the previous May.
The Office for National Statistics also announced that house prices increased by 2.6% in the year to April 2013, following a monthly increase of 0.4% during the month.
The housing market has been boosted by the government's Help to Buy scheme, which gives assistance to buyers struggling to get on the property ladder.
Despite the resulting increase in first-time buyers, Shelter issued an alert earlier this week, stating that young people are increasingly becoming trapped in the private rental market, where they face years of soaring rents, short-term lets, and unexpected letting fees.
LSL said there are now 5% more tenants that there were a year ago, but added that tenant finances are improving, with the proportion of all rent in arrears falling to 8.2% in May 2013, down from 8.4% in April.
David Newnes, director of LSL, which owns lettings agents Your Move and Reeds Rains, said: "Despite a strong increase in new tenants, rents rose more slowly than other household costs. But that demand would have been even stronger had it not been for a recent spurt in the number of first-time buyers.
"Looking further ahead, sustaining the increase in new buyers will depend on how many tenants are able to build big enough deposits to get a mortgage. With wage growth so weak compared to inflation and house price growth, it looks like deposits will become less affordable – which will keep demand for rented accommodation high."