The figure represents a month-on-month rise of 1.2%.
When London is excluded, the average price of rent in the UK is £1,016 PCM – up 1% from the previous month and up 9.5% year on year.
Scotland saw the highest monthly increase in the UK, with rental averages rising by 2.6% monthly.
The UK’s cheapest area, the North East, saw another dip, dropping 2% month on month to £632.
Commenting on the data, Andy Halstead, HomeLet & Let Alliance chief executive officer, said: “Rental prices remain high, which brings a level of risk for both tenants and landlords.
“The London rental market in particular shows no signs of slowing down – there have only been a handful of occasions on which the monthly average has been recorded above £2,000 PCM, with this month’s average of £2,039 PCM going down as the highest ever recorded.
“The fact that the London market is rising in terms of average price while the cheapest area in the country (North East of England) is falling shows that the level of demand somewhat depends on location, but as a broad rule, there is a shortage of rental properties to meet demand, with many prospective tenants facing a real battle to secure a property.
“This frenzied market is likely to see prices continue to rise in the coming months.”