Demand for rental properties seriously outstripped supply during the three months to the end of May, research from the Association of Residential Letting Agents reveals.
The trade body also found rents rose for the fourth quarter running for each type of property, including detached, semi-detached and terraced houses and flats.
As a result of increased demand, void periods have fallen to an average of 24 days.
Over two thirds of all agents in prime central London report rising rent levels.
Half of the agents in the rest of the South East say the same and in the rest of the country the proportion of agents reporting rental rises increased.
Seven out of 10 prime central London agents say there are more tenants than properties.
This is the highest figure seen since the ARLA surveys started six years ago.
Adrian Turner, chief executive of ARLA, says: “There is a shortage of all forms of housing in this country and these results show that the shortage of good quality property is also apparent in the rented sector.
The average value of rented houses rose during the past three months by 2.2% in prime central London, 0.3% in the South East and, by contrast, fell by 3.9% in the rest of the UK.
Average rented house values ranged from 885,000 in prime central London to 229,900 away from London and the South East.
Rented flat values were down, with the average across the country falling by 1.3% during the three-month period.
The value of flats ranged from 501,000 in prime central London to 210,000 in the South East and just 153,000 in the rest of the country.
Despite the rising rent levels, the average yields are down marginally from 5% to 4.8% for houses and from 5.1% to 5% for flats.
ARLA says this reflects continually rising house prices during the quarter.
Tenants continue to stay in rental properties for an average of well over a year.
They remain in the same property for the longest in prime central London at an average of 17.7 months.
This compares to an average of 15.2 months for the South East and 14.2 months elsewhere.
These figures have shown little change for the past two years.
Turner adds: “Even though it still needs more investment, the private rented sector is continuing to provide choice in housing and a safety valve for the housing market, particularly now, at a time of mixed expectations for future strong rises in house prices.”