The average monthly rent being asked of new tenants across Britain, excluding London, has hit a record £1,172 per month.
The number of available homes to rent in December 2022 had increased by 13% compared with a year earlier, while the volume of people inquiring about rental properties rose by 7% over the same period, Rightmove said.
The website predicts average asking rents across Britain for newly available properties will rise a further 5% in 2023, unless there is a significant addition of available homes to rent.
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Rightmove's director of property science Tim Bannister said: "Although the fierce competition among tenants to find a home is starting to ease, it is still double the level it was back in 2019. Letting agents are seeing extremely high volumes of tenant inquiries and dealing with tens of potential tenants for each available property.
"Landlords will need to balance any rent rises with what tenants can afford to pay in their local area, to continue to find tenants quickly and avoid any periods where their home is empty due to tenants not being able to meet the asking rent.
"There appears to be some more property choice for renters compared to the record low levels of last year which would slightly ease the fierce competition to secure a home.
"This is why we're forecasting that the pace of annual growth will ease to around 5% by the end of the year nationally, although this would still significantly exceed the average of 2% that we saw during the five years before the pandemic."
James Redington, sales and lettings director at Douglas & Gordon, said: "We've seen the highest rent increases we've seen for decades, and we don't expect this to slow down in the short-term."
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