The man attacked his 10th known victim, a 14-year-old girl, in Hertfordshire on Friday.
The attacks began in the south-east of England in November 2001 and the rapist's victims have ranged in age from 10 to 52 years old.
Description of the serial rapist
White
Aged 30-50
5ft 5in to 5ft 10in tall
Medium to stocky build
Tanned, leathery skin
Short dark hair, greying in places
Gruff voice with north-east accent
The officer leading the hunt, which is codenamed Operation Orb, warned women not to wear headphones while walking in secluded areas so they could remain vigilant.
Kent Assistant Chief Constable David Kelly said the man was "extremely dangerous" and appealed for anyone with information to contact police.
"This man's rapes are horrible offences by any definition, the rape of children, girls of 10, 12, 13 or 14-years-old, right up to a woman of 52," he said.
"This is a man who is more than likely to strike again and we need the public's assistance to catch him as quickly as we can."
Detective Superintendent Mark Warwick, the deputy investigating officer in the case, said: "This person has a distinctive description.
"There's distinctive things about his accent, he's a smoker, a drinker and he has tanned, leathery skin.
"When you put all these variables together, we're not actually looking at the whole population of the UK.
"We're looking at a very small group of people and someone, somewhere knows this person, either as a friend, a partner or an ex-partner."
Friday's attack in Hertfordshire followed five in Surrey, two in south London and one attack each in Kent and Berkshire.
Despite being spread out, police say there are similarities in the locations where the rapist strikes.
Mr Warwick said: "He is striking on footpaths close to wooded, bracken type areas, but near to housing estates.
"So it's not in rural locations, it's in urban surroundings that this person operates."
Police have received more than 1,000 responses from the public which have led to a "number of active lines of inquiry".