Private sector rents in September were 4.6 per cent higher than a year earlier at £968 per month on average, marking the strongest growth in 13 years.
The fastest rice since 2008 comes as strong demand outstrips supply, according to an index.
Excluding London, rents across the UK were up by 6 per cent annually, a figure which Zoopla said was a 14-year high.
But rents in London are now also starting to climb as people return to offices, with annual price growth of 1.6 per cent recorded in the latest report, compared with falls of nearly 10 per cent at the start of the year.
Rents in the South West of England were up by 9 per cent annually, making it the region registering the fastest rental growth in the third quarter of 2021.
And rents in Purbeck in Dorset were up by 16.2 per cent annually, making it the location with the highest rate of rental growth.
Zoopla said demand is continuing to outstrip supply and putting an upward pressure on rents.
Rental growth is also partly due to the popularity of properties in higher price bands, reflecting an ongoing search for space during the coronavirus pandemic.
Annual growth in rental prices stood at 2.7 per cent in Scotland (averaging £627 per month), 5.8 per cent in Northern Ireland (£633 per month typically) and 7.7 per cent in Wales (£660 per month).
Grainne Gilmore, head of research at Zoopla said: “The swing back of demand into city centres, including London, has underpinned another rise in rents in quarter three, especially as the supply of rental property remains tight.”
She added: “Meanwhile, just as in the sales market, there is still a cohort of renters looking for properties offering more space, or a more rural or coastal location.”
Commenting on the findings, Richard Davies, Head of Lettings at Chestertons, said: “This continued surge in demand, especially in Prime Central London, is heavily impacting the supply of available properties to rent in the capital.”
“As a result, rents have risen sharply and tenants now have a much more limited choice than they did last year. On average they are only able to view one or two properties that meet their criteria, which greatly differs from a year ago when they were able to view at least five,” he said.
“With demand outstripping supply, landlords are currently in a strong position and those who have been considered selling their property may be persuaded to keep it as a rental investment given that rental yields are now increasing,” Davies concluded.