The average rent has hit a record high outside London and stood at an average of £1,162 per calendar month in the three months between July and September.
Rent prices in London had their greatest ever annual increase, rising 16.1% to an average of £2,343 a month during the period, according to an analysis of 357,061 rents advertised on Rightmove, the real estate website.
Nationally rents rose by 3% in the three month period for only the third time on record.
Everywhere in Britain had an increase in the number of rental properties available except for London where there was a 24% decline in the number of rental properties available.
Meanwhile, demand for rental properties was up 20% across Britain compared to last year while the number of properties available to rent was down 9%.
As a result, competition for properties is "extreme", Tim Hassell, director at Draker Lettings in London said.
"Within a few hours of a property going live, we are receiving dozens of enquiries which, when compared to the pre COVID market, is extreme.
"Previously we would receive between 5-10 enquiries in the first 48 hours and now we are receiving 30-40 in the same time frame. This has also resulted in multiple offers from tenants who are competing by paying over the asking price and offering significant funds up front."
The regions which had the greatest number of new rental properties were the South West (with a 19% increase), Yorkshire and The Humber (a 12% increase) and Wales (a 10% increase).
The rise in mortgage rates experienced since former-Chancellor Kwasi Kwarteng's mini-budget is also increasing rental demand.
The analysis suggested that first time buyers may wish to extend their tenancy rather than buy a property, adding to the demand for rental properties.
Renting is a cheaper option than home ownership for first time buyers due to increased mortgage costs: The average monthly mortgage payment for a new first-time buyer putting down a 10% deposit is now a fifth (20%) more than the rental payment for the equivalent type of property, the Rightmove analysis said.
Rightmove's director of property science Tim Bannister said: "Those looking to rent a smaller property in the next few months may find that they face some added competition from would-be first-time buyers, who have had their purchase plans scuppered for now due to the sudden rise in mortgage interest rates, and are now looking to rent."
As cost of living pressures mount, renters have been looking to downsize and demand for smaller properties has grown.
In particular, demand for studio flats increased from July to September.
There were four times as many tenants looking for a studio flat as there are studio flats available, a 71% increase on a year ago, the data showed.
City centre locations proved increasing popular.
John O'Malley, CEO at Pacitti Jones in Glasgow, said: "The dramatic rise in the cost of living means that we are now starting to see older people downsizing to apartments to reduce household bills - and being centrally located they will also reduce travel expenses. And this is something we expect to see more of."