According to figures published by the Valuation Office Agency, a division of HM Revenue & Customs, the cheapest quarter of rents in the capital increased by 8.8% in the year to June 2012.
The median monthly rent for London grew by 6.8% over the year to hit £1,148, double the national average.
The dramatic increase was driven by a surge in the cost of family homes, with rents for properties of four bedrooms or more in the bottom quarter of the market increasing by 8.3% over the year to stand at an average of £1,625 a month. Rents for rooms, studio flats and one-and two-bedroomed apartments increased by more than 5%.
Many of the households in the bottom quarter of the London market receive housing benefit, which is capped at £250 a week for a one-bed flat and £400 a week for a four-bed house.
According to the Chartered Institute of Housing there are 281,000 households in London receiving benefit for private rented homes, while only 205,000 properties have rents at or below the cap.