The Association of Residential Lettings Agents (Arla) said that 39% more agents reported that demand had outstripped supply in the last three months.
Greater London and the South East saw the biggest imbalance.
But Arla said rents were falling as there had been a surge in the number of new two-bedroom flats coming onto the market.
In May, Capital Economics, a London-based consultancy, forecast that rents would rise by between 10% and 11% over the next two years.
The Arla research, based on responses from 444 letting agents, showed a fall in the average length of time that a property remained empty between tenants, dropping from 24 days to 22 during the last three months.
It also found that 77% of landlords said they were not planning to either buy or sell properties in the near future.
In the course of the last week, major lenders including Nationwide, Abbey and Bradford & Bingley have increased the rates of new mortgage deals.
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