Police are investigating the murder of Sian and their two sons Zachary, eight, and four-year-old Amon after three bodies were discovered in the back garden of the house in Erith, south east London, earlier yesterday.
A source told the Sun that 'Interpol have been informed and there is an alert out to find him.'
On Monday, Simpson-Kent’s ex-wife Dominique Deblieux claimed he was a violent coke dealer who beat her and their daughter.
Speaking from her home in Cagnes-Sur-Mer, southern France, she said:
“He smoked cocaine on many occasions and dealt a little in it too. I’m wondering now whether drugs lie behind what he is supposed to have done in England.”
She added that their marriage was a “waste of time” and he “didn’t really care” for his daughter Isis. “He was a violent man towards me,” she said, claiming that he had eight children by several women.
She said: “I said ‘Hi’ but she ignored me. The talk was she had been beaten up, that she was trying to cover up her injuries.”
The day after Sian was last seen alive, Simpson-kent was allegedly seen alone at the house filling Sian’s Renault Scenic with black bin bags and the boys failed to turn up at school.
It is believed the Samaritans alerted the police to his well-being and when they arrived he reported his partner and sons missing.
Last night it was reported relatives received text messages from Sian’s phone saying she was okay and wanted to spend one last Christmas with the boys after she disappeared.
It is believed they were sent by Simpson-Kent while he was in the Colchester and Cambridge areas on the way to Glasgow, before Simpson-Kent is believed to have fled to Ghana.
Police are understood to be probing claims he was spotted clearing out the house with bin liners before he disappeared and also carrying out ‘cell site’ analysis on his mobile phone to piece together his movements.
Det Supt Monk, from the Met Police, said: "Our efforts are continuing to find Arthur Simpson-Kent.
"Our appeal is to anyone who may know his current whereabouts or can assist us in finding him - we do need to speak to him as a matter of urgency."It comes as it was revealed that the Metropolitan Police could be referred to the Independent Police Complaints Commission over its handling of the case.
A Scotland Yard spokesman said: "The case has not been referred to the IPCC at this stage.
Ms Blake - who played homewrecker Frankie Pierre in the BBC soap in the mid-1990s - was last seen alive after visiting relatives in Leyton, east London, with her sons on Sunday December 13th.
Sian's car was found abandoned in Bethnal Green, east London, over the weekend.
Police say it is not known why the vehicle was parked there and by whom.