But detectives still believe that Victor Farrant, 45, also wanted for questioning over the attempted murder of another woman, is probably still in Britain, although there are concerns that he may have fled to Europe.
A national and international alert was posted on Thursday after the body of Glenda Hoskins, 45, was found wrapped in a carpet in her apartment in Port Solent, near Portsmouth.
Detective Superintendent David Hanna, who is heading the murder investigation, said it was possible someone was sheltering Farrant.
"If he is that smooth and persuasive to people he could easily make contact with somebody else, and we would hate to think another serious crime could be committed," he said. "He may enjoy the notoriety."
Mrs Hoskins is thought to have been suffocated. She was trying to break up with Farrant, whom she had been seeing for about four months.
Police say there is an evidential link between Farrant and a knife and bottle attack on Ann Fidler, 43, who ran an escort agency from her home at Southampton Road, Eastleigh, Hampshire. After the attack last December, she underwent emergency surgery, but because of brain damage has no memory of what happened.
Police have managed to trace some of Farrant's trail, following the murder of Mrs Hoskins.
Driving her car on the day of the murder last Wednesday he was seen in Portsmouth and, later in the afternoon, at Brighton, Sussex, where he has lived and worked. On Friday the vehicle was found parked at Plaistow, east London.
Detectives have not ruled out the possibility he may have fled abroad, and have called on Interpol to help in the search. He lived for several years with his former wife in Belgium.Reuse content