Average advertised rents were 3% higher than a year earlier, with a constrained supply of homes contributing to rising rents, Rightmove said.
While the number of available homes to rent across Britain is 8% higher than a year earlier, it is still 27% lower than in August 2019, the website added.
Average advertised rents are rising fastest in the north-west England, with average rents around 10% higher than a year earlier, and slowest in London, where average rents are 2% higher annually.
Colleen Babcock, a property expert at Rightmove said: “There are challenges for both tenants and landlords in the current market.
“While tenants looking to move have more choice and less competition from other tenants compared with a few years ago, some may still find their options limited with rents at record levels.”
She added: “Landlords provide vital homes to tenants and have already faced an increase in taxation through stamp duty changes.
“It is essential that it remains attractive and viable to be a landlord so that tenants have comfortable places to live.
“If more landlords are driven out of the sector by more and more taxation, it will be tenants who lose out in the long run.”
Here are average advertised rents per month in August and the annual increase, according to Rightmove:
East Midlands, £1,134, 2.3%
East of England, £1,599, 2.5%
London, £2,699, 2.0%
North East, £918, 2.9%
North West, £1,278, 9.7%
Scotland, £1,141, 2.4%
South East, £1,828, 2.4%
South West, £1,461, 2.1%
Wales, £1,107, 2.6%
West Midlands, £1,196, 2.5%
Yorkshire and the Humber, £1,051, 2.5%