The average UK rent is now £669 but still remains 2.5% lower than a year ago.
The strongest growth over the last three months has been in London and the South East where rents rose 4.5% and 6.5% respectively, equivalent to annual climbs of 19% and 29% respectively. By contrast, several regions are still seeing rents flatlining.
In the South West, Yorkshire & the Humber, the West Midlands and the North East, rents are treading water or slightly lower.
David Brown said: "High inflation allowed landlords to keep rents rising for almost a year after house prices began to fall, but they have been pretty quick to start increasing them again too.
"The key is tenant demand. Only 166,000 first-time buyers have bought a home in the last 12 months, frozen out of the market by lenders restricting mortgage availability, despite homes being more affordable than any time since 2003.
"There are 200,000 fewer first-time buyers than the average for the last few years. These people are accumulating in the private rented sector, keeping demand high and allowing landlords to keep rents relatively high too.
"Almost two fifths of the UK’s tenants live in London and the South East, where house prices are highest, and supply is most constrained. Unsurprisingly, landlords therefore have greatest pricing power in these regions so rents are now rising rapidly. The housing market recovery began in London and the South East and the rental market is now following suit.
"Many landlords are also struggling to get a mortgage too – the CML’s figures show only a third as many buy to let loans were made in the first half of this year compared to the year before. That is further restricting supply in the private rented sector at a time of real housing need and is causing rents to rise faster than they would otherwise do."
But he added: "There is no evidence yet that rising rents are leading to higher arrears as the number of tenants falling behind with their rent is steady as a proportion of all tenants.
"In fact the trend remains on a downward path after arrears peaked in February this year. The key is the tenant mix. The large increase in high quality would-be first-time buyer tenants with solid finances means that rent is more likely to be paid in full and on time."
Have your say on this story using the comment section below