Rental growth on renewals rose faster than new lets last month, says Hamptons.
Tenants staying put saw rents rise by an average of 3.7% to £1,267 per month in May.
Even so, this leaves the average tenant renewing a contract paying £99 per month less than a tenant moving into a new home.
The average rent on a newly let property in Great Britain rose 1.5% over the last 12 months to £1,366 per month.
This means rents are growing at a similar pace to 2013, when they rose by an average of 1.6%.
In May 2024, average rents increased by 5.1% annually, so the pace of growth has declined by nearly two-thirds over the last year.
For tenants moving into a new property, rental growth remains highest in the North and the Midlands.
Meanwhile, London rents fell 0.5% on the same time last year, reducing the headline national rate of rental growth by 1.0%.
Rents in the capital now stand below where they were in June 2023.