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."

Emma Way, 22, from Norfolk, was found guilty at Norwich Magistrates' Court of failing to stop after a collision and failing to report an accident.
She was cleared of driving without due care and attention.
Way said that following the "stupid" #bloodycyclists tweet there had been lots of "malicious messages".
Magistrates heard that police only became aware of the collision on 19 May because Way, from Watton, tweeted "definitely knocked a cyclist off his bike earlier. I have right of way - he doesn't even pay road tax!" using the hashtag #bloodycyclists.
Cyclist Toby Hockley, from Norwich, suffered bruising and minor damage to his bike in the incident near the village of Rockland All Saints, Norfolk.
Appearing on ITV's Daybreak programme earlier, Way said that she regretted the Twitter post but did not believe the collision was her fault.
She said: "I am 22, so not generalising on 22-year-olds sometimes you do just put things and it's not actually intended.
"I was quite angry at the mannerism of the cyclist on the road. My point of view is that he was on my side of the road - that's not the way you drive so I find that quite disrespectful."
CTC, the national cycling charity, said the collection of evidence around cycling incidents should be more "robust".
Rhia Weston, a road safety officer with the charity, said: "The only reason Emma Way was caught was because she tweeted about the incident, many other hit and runs end in no prosecution because police fail to trace the driver.
"Evidence collection needs to be much more robust if hit and run drivers are to be caught, prosecuted and convicted.
"CTC's Road Justice petition is calling on the police to better enforce road traffic law by thoroughly investigating all injury collisions."
Way, who said she did not receive a fee for the television appearance, was sacked from her job as a trainee accountant with Norwich-based Larking Gowen after the tweet.
The court heard she has now got a new job.
Magistrate Martin Cliffe fined Way Â£337 and ordered her to pay Â£300 in costs. He also ordered that seven penalty points be added to her licence.
Ms Weston said Way's sentence was "minimal" compared to "the maximum sentence the judges had at their disposal of Â£5000, six months custodial sentence, a discretionary driving ban and 10 penalty points".
"A tougher sentence would send a clearer message that disregard for other people's wellbeing on the roads is intolerable..."
Way previously described her tweet as her "biggest regret" and rated it "11 out of 10" on the stupidity scale.
She told Daybreak: "I lost my job in accountancy and I've received really malicious threats and stuff off people... cyberbullying and stuff, so it has been quite bad."
Way had about 200 Twitter followers when she sent the message and used to tweet daily.
She has since quit the social networking site.
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.
[NEXT_CONCEPT]
A motorist convicted of driving offences after tweeting about a collision with a cyclist says she has been cyber-bullied because of the post.