The rapist has struck 20 times in the past seven years, always attacking women aged at least 70 living alone and asleep in bed.

An 82-year-old from Croydon and an 88-year-old from Orpington were raped in the last few months. The oldest rape victim, an 89-year-old from Croydon, was attacked in 1992.

'Vulnerable, elderly women'

Scotland Yard said it was confident that the rapes, as well as an attempted rape and 16 burglaries with an "element of indecency" in a 14-mile band from Warlingham to Bexley, south-east London, were linked.

In every case, the man broke into the victim's house through a ground floor window.

"These are attacks on vulnerable elderly women," said Det Ch Insp Duncan Wilson, leading the inquiry. "While such attacks are rare, I would like to catch this man before he can strike again."

Mr Wilson said he would like to speak to anybody who recognised the man in the e-fit.

A reward of £10,000 has been offered by detectives for information leading to the arrest and conviction of the man.

Police also released a video of a man seen near houses of elderly residents in Croydon, but police said he might be an innocent bystander and were keen to eliminate him from inquiries.

"It may be he had a genuine reason for being there and I would urge him to come forward," said Mr Wilson.

The rapist is aged about 25-35 and spoke to the four victims of his most serious assaults with a soft voice.

Active at night

He is black, possibly of mixed race, between 5ft 8in and 6ft 1in in height and was wearing dark clothing.

"He is active in the middle of the night," said Mr Wilson. "Someone must be aware of this night-time activity. It may be that his day-time work is suffering."

Detectives believe the rapist could have been abroad or in prison after the first attack.