The average rent stands at Â£774 in England and Wales, according to data from Your Move and Reeds Rains.
It said that rental costs had risen by 0.8% in April compared with March.
Adrian Gill, LSL director, said: "Momentum is fuelled by a fundamental shortage of housing and given oxygen by renewed wage growth."
The latest official figures from the Office for National Statistics (ONS) suggested that the cost of renting a home from a private landlord in Britain rose by 2.1% in the year to the end of March.
Campbell Robb, chief executive of housing charity Shelter, said: "Our housing shortage has been decades in the making, and only bold and immediate action can fix it.
"No matter how hard they work or save, an entire generation is being forced to watch their dreams of a stable future slip through their fingers, stuck in properties where rents eat up their salaries and short term contracts leave them with no stability at all."
The cost of renting a home rose by 4.6% in the year to the end of April, the fastest rise since November 2010, property group LSL has said.