This has pushed the typical rent to £1,078 per month, Zoopla said.
The website said this equates to 35% of the average income of a single earner – the highest level in more than a decade.
These cities are seeing demand exceed supply, being major employment centres with large student populations, it said.
The report said there has been a modest increase in rental supply in recent weeks, as the house sales market has weakened.
The average number of homes for rent per estate agency branch is 10, up from seven at the end of September, Zoopla said.
Richard Donnell, executive director at Zoopla, said: “A chronic lack of supply is behind the rapid growth in rents which are increasingly unaffordable for the nation’s renters, especially single-person households and those on low incomes. Many are also staying put to avoid the worst of rent increases.
“Renters are having to adopt a range of strategies to deal with rising rents.
“We have seen a rapid increase in demand for one and two-bed flats while some renters are now considering sharing a property to cover the cost of rent.
“Others may now need to stay at home with parents or relatives for longer until they can afford to rent privately.”