A mother and her eight-year-old daughter found the murdered victim in a lift in their block of flats near Waterloo Station in London.

A man in his 30s was arrested nearby and is being held for questioning at a south London police station. Scotland Yard refused to comment on reports suggesting he was the victim's boyfriend.

The girl was wearing her school uniform, local residents said. She had reportedly been stabbed at least 10 times.

Paramedics tried desperately to revive the girl but she was pronounced dead at the scene. She was the 16th teenager to die as a result of violent crime in the capital so far this year.

Police are keeping an open mind about the motive for the killing at Matheson Lang House, in Baylis Road, south London, but do not think it was gang-related.

Meanwhile, Home Secretary Jacqui Smith urged mothers to sit down with their teenage children to warn them about the dangers of carrying a knife before it is "too late."

Speaking on GMTV, Ms Smith outlined measures to tackle knife crime, including an advertising campaign aimed at deterring young people from carrying knives and knife arches and wands.

Asked about the stabbing of the 15-year-old schoolgirl in London and of anti-gun campaigner Pat Regan in Leeds, Ms Smith said events such as these were worrying.

She said: "It is these sort of events that make us all feel worried and want to redouble our efforts."