A report by Rightmove gives some hope of an easing ahead as higher mortgage rates alongside the cost of living crisis all combine to squeeze affordability.
Average rents for properties across Britain have hit a new record high, according to data from a property website showing a record £2,500 per month in London.
Rightmove said the average rent being asked outside the capital topped £1,190 per month for the first time during the first three months of the year.
It completed, the company said, a rise in rents outside London during every quarter since the end of 2019.
The main reason why rental costs have climbed so steeply has been demand outstripping the supply of available properties.
This was exacerbated last September when the financial market chaos that followed the Liz Truss government's mini-budget prompted a temporary spike in mortgage costs.
The fallout has contributed to a sharp easing in annual house price growth.
Agents and landlords have been inundated with enquiries while some have been able to lock in longer, more lucrative tenancy agreements of up to three years due to the high demand.
Rightmove said the largest imbalance between supply and demand was in the terraced houses sector.
But it added there was evidence that the pace of rental price growth was easing due to an increase in the number of rental homes becoming available this spring.
The website's director of property science, Tim Bannister, said: "We have seen some early signs of improvement on squeezed supply levels this year, though with no significant influx of new properties becoming available to rent currently on the horizon, the mismatch is set to continue for some time.
"Many agents are having to manage a very high volume of tenant inquiries for every property that they let in the current market.
"Properties in popular areas within an affordable asking rent range of that local area are likely to be snapped up almost immediately, and on average homes are finding a tenant much more quickly than this time in 2019."