The South East was the only part of the UK where rents fell last month.
The average rent for the region came in at £997 per month, down by 0.3 per cent year-on-year, according to data from HomeLet.
In London, the average rent for new tenants in March was £1,546 per month, an increase of 1.2 per cent on the same month the year before.
Martin Totty, chief executive of HomeLet, said: "In the current housing market, where demand for homes continues to outstrip supply and house prices are out of reach for many buyers, the long-term trend in the private rental sector is likely to be for rental price inflation to continue."
However, he said landlords were keen to make sure rents were affordable, with rent rises now far below the overall rate of UK inflation.
The rental sector has come under significant government regulation in the past few years. Around this time last year, the rate of stamp duty on second homes was hiked by three per cent, a measure intended to cool down buy to let investment.
Then, chancellor Philip Hammond introduced a ban on letting agents fees for tenants. He argued that landlords should be paying these fees, and that often tenants were being charged extortionate amounts by rogue letting agents.
Landlords were outraged by the changes, and threatened to increase rents in retaliation. However, a landlord survey from HomeLet has found that nearly a third of landlords do not intend to increase rents this year.
Speaking to the communities committee this week, housing minister Gavin Barwell defended the regulation.
He said given the imbalance of supply and demand in the rental market, renters were in a comparatively weak position, and would not be able to negotiate fair rates from lettings agents. Therefore, it was right for the government to intervene to protect them.