According to data from Homelet, rents agreed on new tenancies in the UK over the past three months increased by 2.3 per cent as compared to the same period last year - excluding London.
Rent increases were far higher in the capital, rising by four per cent in the three months to the end of July compared to the same three months in 2015.
Martin Totty, Barbon Insurance Group's chief executive, said: "Ultimately, rents will be determined by supply and demand in the private rental sector; what we know here is that population growth will continue to increase demand, and that the housing stock isn't growing quickly enough to meet that demand."
He said rents would continue to climb - albeit at a lower pace than previously.
On the Brexit vote's impact on the market, Totty said: "It seems likely that with lenders concerned about the prospect of falling house prices, loans to value in the mortgage market are going to become less generous, which may see more people turn to the rental sector rather than buying a property."
The data largely mirrors what has been happening to house prices, with price growth slowing throughout the year, before entering negative territory in July.
The most recent house price index from Halifax showed that house prices fell in July - although commentators could not agree on what the data actually meant for the market.