The shocking sum comes as renters in the capital face rising prices and intense competition for rooms.
New figures from Foxtons show rents rose in September after falling in August following the record amount of £549 set in June when landlords raised rents.
Supply issues are still a prevalent issue across London.
In September, there was an average of 29 rents for each property – with many private landlords expecting bidding wars over properties.
This figure dropped slightly from 33 applicants per property in August, but is still higher than Foxtons reported for the three preceding years.
Renters also spent an average of 101% of their registered budget in September 2022 – a rise of 3% from August.
Central London continues to be the most expensive area for weekly rents this year – at £636. This is an increase of 30% on prices reported in 2021.
Gareth Atkins, managing director for lettings at Foxtons, said: “The lettings market in September continued to grow as we hit a new record high for the average rental price.
“This demand was triggered by huge numbers of new renters looking for property: students physically returned to London post-Covid, corporate relocations resumed at full pace and rising interest rates persuaded some buyers to continue renting in the immediate future.
“It meant, in September, 29 applicants registered for every new property brought to the market.
“Combined with this, there were 38% less new market listings than the same time last year.
“With over three quarters of our tenants choosing to renew rather than look for a new property, I don’t expect the pressure of low stock to ease anytime soon.”
The most competitive region of the capital was south and east – with an average of 37 applicants per instruction.
But North London also saw the largest monthly increase of 20% more applicants per instruction.
Renters’ average weekly budget was £494 in September 2022, just slightly lower than the £500 per week seen in August 2022.
However, budgets were 6% higher compared with the same month last year.
Central and East London continued to have the highest year-on year increase, at 12% and 11% respectively.
August and September are typically the peak for the lettings season each year – with August this year recording the highest level of demand ever reported.
Average rents also broke records in September at £553.
There were also 23,000 new listings on Foxtons in September – the lowest monthly volume of new instructions in 2022 so far.