The average monthly private sector rent across England and Wales in May was £792, marking a 0.2% fall compared with April, the report from letting agents Your Move and Reeds Rains found.
On April 1, a three percentage point stamp duty hike was imposed on investors purchasing buy-to-let properties. Estate agents previously reported seeing a rush of landlords snapping up properties to beat the deadline.
The report said that many of these properties bought by landlords are now starting to appear on the rental market. With more properties available for tenants to choose from, this has helped to ease the upward pressure on rents.
Adrian Gill, director of Your Move and Reeds Rains, said: "A tide of new properties to let has disrupted the normal dynamics of supply and demand.
"Landlords escaping a much larger stamp duty bill by completing their purchases before April 1 have now finished their repairs and paperwork, with these homes to let competing for tenants in May and into June. That short-term mismatch has made May an exceptional month, with excellent deals available for some prospective tenants."
Across the country, rents have increased by 1.8% over the last year, which is half the 3.6% annual rate of growth recorded in January 2016.
But Mr Gill said that in the longer term, with landlords also facing tax changes that could eat into their profits, there could be a "drought" of homes to let that will push up prices for tenants.
He said: "All tides go out again - and this is definitely no exception. Overall the tax changes to the buy-to-let industry will discourage some property investors, and most of the properties that became available to let in May will have been planned purchases brought forward from later in the year. The net effect will not be more properties to let - quite the opposite."
The index, which is based on rents achieved on around 20,000 properties, found that rents in London fell by 0.7% month-on-month in May to reach £1,220 per month on average. This was the steepest fall of any region.
At the other end of the spectrum, rents in Wales increased by 1.4% month-on-month, taking the average rent there to £559 per month.
Despite the general dip in rents in May, tenants' finances worsened, with 9.3% of all rent due being late, compared with 8.1% in April.
The report said that while tenants have become more likely to fall a little behind with their rent by one day or more, the chances of tenants developing more serious financial problems have fallen. In the first three months of 2016, tenants were less likely to fall two months or more behind with their rent than they were in the last three months of 2015.
Mr Gill said: "There's no room for complacency. Rents have dipped unexpectedly in May but remain far higher than in previous years, while household earnings have lagged the wider recovery for some time. Landlords need to be aware of such risks - and always keep lines of communication open."