Sian Blake, 43, who played Frankie Pierre in the soap, went missing from Erith, Kent .
She was last seen on Sunday 13 December in Waltham Forest, east London, with eight-year-old Zachary and four-year-old Amon.
Officers believe they are still in the London area - but Ms Blake also has links to Cambridge and Colchester.
Relatives have received text messages from her but she has not been seen since she went missing, the Metropolitan Police said.
The force added: "Officers are increasingly concerned for Sian and the children's wellbeing."
Ms Blake reportedly suffered from motor neurone disease and had been "looking very thin and frail" before she disappeared, her neighbour Sandra Metzgen told The Sun.
The actress appeared in 56 episodes of EastEnders between 1996 and 1997, according to the IMDb website.
She is described as being black, 5ft 2in and slim with short black hair.
She wears glasses but can also wear contact lenses.
:: Anyone with information should call police on 101 or Missing People on 116000, quoting reference 15MIS050346.
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