Rental demand is up 21% year-on-year, according to the latest research by Zoopla.
In addition, houses for rent are letting 30% faster than one year ago.
As lockdown restrictions are eased in city centres rental prices have fallen, with Edinburgh noting the greatest decline at -1.8%.
Greater Manchester followed, down 0.9%, and average prices in Greater Birmingham dropped by 0.8%.
However across the UK as a whole, excluding London, rents are up 2.3% which is aligned to pre-COVID levels.
Overall since the global financial crisis, London has seen the biggest decline in rental prices annually, down 8.3%.
The downturn is easing however according to the research, and the -0.4% price decline recorded in December is the most modest monthly fall since pre-pandemic.
New supply in London is up 30% year on year, primarily driven by more and more short-lets being transitioned into long-lets.
Flexible working is likely to result in a permanent shift in priorities for some renters, while the demand for space is likely to hold firm, supporting the family homes rental market, the firm outlined.
Grainne Gilmore, head of research, Zoopla, said: “Changing working, commuting and tourism patterns were felt very quickly in the central London rental market.
“Now we are seeing the impact in other city centres, although on a more modest scale.
“Balancing the rental declines in inner cities is the strong rise in rental growth in surrounding ‘halo’ areas and well-connected towns across the UK, reflecting stronger demand in many of these markets among a cohort of renters.
“Yet it is important to note that most demand among renters living in central cities is within the same area – some renters will have ties to an area through schooling, or non-office based work.
“The search for space among renters is coming across loud and clear from the data however, with houses in major cities now being rented out more quickly than a year ago. In most cases, flats are now taking longer to rent out.”