The 20.9% increase is the fastest of any region in England and almost double the national average rise of 12.5%, according to the Office for National Statistics (ONS).
It is also six times that of the North East (3.4%), where rents have risen the slowest.
Separate ONS data highlighted how the average household's disposable income has risen by just 4% between 2010 and 2015. This means that, in many parts of England, it has not kept pace with rental rises.
Campbell Robb, chief executive of housing charity Shelter, said many households were struggling to keep up with the "relentless" hikes.
"Millions of private renters are bearing the brunt of our housing crisis, forking out a huge chunk of their income for rent each month and coping with relentless rent rises.
"Every day we hear from families stuck in the rent trap - left with no choice but to stay in expensive and unstable private renting, and unable to save for a stable future in a home of their own.
"We have shown that Government schemes like Starter Homes will only help the well-off, not the majority of Generation Rent who are working hard for average wages.
"If the Chancellor is serious about fixing our drastic housing shortage and giving hope to the country's struggling renters, he must invest in the genuinely affordable homes we so desperately need."
Below is the change in average rents for private housing in England since September 2010:
- London: 20.9%
- SE England: 11.9%
- Eastern England: 8.5%
- SW England: 8.3%
- East Midlands: 7.2%
- West Midlands: 6.7%
- Yorkshire & the Humber: 4.4%
- NW England: 3.9%
- NE England: 3.4%