A recent LSL Property Services survey says 'gazumping' is pushing up rents in England and Wales as the average cost of renting hit £696 a month in May - £4 higher than the previous month.
Rising demand from tenants has led to some offering above the asking price to rent a home.
The average cost of renting a home has now risen 4 months in a row.
However, more than one in ten tenants in the UK missed or were late paying their rent in May, the survey found.
The survey said that typical rent was 4.4% higher than a year earlier, but there were significant regional variations.
In London, annual rental costs have risen by 7.8% in the last year. In the North East rents are up 6.4% and the East Midlands saw a 6.2% rise.