Police have made a second arrest in their investigation into the murder of two French students in a frenzied knife attack in London after a man handed himself in to police, authorities said on Monday.

Bio-engineering students Laurent Bonomo and Gabriel Ferez, both 23, were bound, gagged and repeatedly stabbed in Bonomo's south London apartment in what police said were the most "frenzied, brutal and horrific" murders they had seen.

"A 33-year-old man handed himself in at a south London police station early this morning where he currently remains in custody," Scotland Yard police said in a statement.

Monday's development follows the arrest of a 21-year-old in connection with the murders over the weekend. The detainee was released without charge on Sunday.

Police have issued a computer-generated likeness of a man seen running away from the vicinity of the apartment on the night of the murders.

Witnesses described him as white, aged between 30 and 40, slim build and wearing a light coloured baseball cap, dark top, blue jeans and white trainers.

Bonomo was stabbed nearly 200 times, with up to 80 of the wounds inflicted after he was dead. Ferez received nearly 50 knife wounds.

The killer or killers then set fire to the apartment in what police said was an attempt to destroy evidence.

A black Packard Bell laptop computer was stolen from the flat six days before the murders. Bonomo disturbed an intruder who stole the laptop as he took an early morning shower.

Forensic experts have found no evidence of forced entry after Sunday's murders, suggesting that a set of keys might also have been stolen to gain entry on the day of the killings.

Two Sony handheld games consoles were also taken that day. Credit cards are also believed to be missing.

French newspapers said the shocking murders highlighted how dangerous London has become after a spate of teen stabbings this year that has prompted the mayor to make it a priority and police to expand a specialist knife-crime squad.

Eighteen teenagers have been knifed to death on London's streets this year.

London police have arrested more than 1,200 people and seized 528 knives during a six-week crackdown sparked by the growing number of stabbings.