Claire Tiltman staggered out after being stabbed several times and died beside a busy road in the evening rush hour on Monday.
Detective Superintendent Owen Taylor said: 'It appears to be a totally senseless, mindless act of violence. There was nothing to indicate robbery was a motive and there was nothing to indicate that it was a sexual attack.'
Claire left her home in Horns Cross, near Dartford, Kent, at 6.10pm to walk to a girlfriend's house in Greenhithe, about one and a half miles away. She was within a quarter of a mile of her destination when the attack happened 15 or 20 minutes later.
The alley led from London Road, the A226 between Dartford and Gravesend, to Ivy Close. Det Supt Taylor said: 'We are desperately seeking the help of the public. There were an awful lot of people in that area.'
Claire was 5ft 1in tall with brown shoulder-length hair. She wore black ski pants, a white rollneck sweater and a brown suede jacket with zip-up front.
Police are looking for a silver VW Golf, thought to have a T registration, seen parked near the alley with its hazard warning lights on about the time of the murder.
They also want to trace the driver of a white Allegro and a man who was wearing a white trenchcoat. Anyone travelling along London Road between 6pm and 6.45pm should contact police.