Spanish police have been asked to help to trace the mother, Yasmin Gibson, 34. Her daughter, Gemma, who attends a private theatrical school, was taken into care by Hammersmith and Fulham social services on Tuesday.
The council said it appeared no child care arrangements had been made. Neighbours said that the child - who has appeared in television commercials - had been left by herself in the two-bedroom flat on previous occasions.
A spokeswoman for Hammersmith council said: 'We originally arranged for the girl to stay with a neighbour, who has apparently looked after her in the past. When the woman fell ill, we took her in.'
The alarm was raised by the caretaker of the large 1930s mansion block of flats, Jim Chapman, who said he called round to see the girl the day after her mother left, after being told that she might be living alone in her third floor flat.
She was looked after by the elderly neighbour for a week and it is believed she spent only one night on her own.
Hammersmith council obtained a High Court injunction preventing the girl being named but it was lifted last night after Mr Justice Hollings was told she had already been named in the London Evening Standard. She was made a ward of court. The girl is now living in a local children's home.
Sir Robin Phillips, owner of Ravenscourt Theatrical School in Hammersmith, said that the girl had continued to attend the school while her mother was away.
'She appears to be all right, although it is obviously stressful for her. She has turned up every day looking clean and tidy with her lunch money. Her fees have not been paid for this term, but that is not unusual.'
Ms Gibson apparently told friends that she expected to be away for three or four weeks. She is understood to have called her daughter the day after she arrived in Spain, but to have made no contact since.
Scotland Yard said that police were anxious to interview the mother. The child protection team at Hammersmith is investigating the case in conjunction with social services.
Sir Robin said that Gemma had been at the school for three years. 'She is a talented little girl and a hard worker. She is a good actress and singer and has a particular flair for dance.
'She has been doing a voice- over for a commercial for a magazine today, which will keep her mind off her problems.'
He described her mother as 'very pleasant'. 'This seems to be completely out of character. My guess is that she has had some sort of breakdown and gone abroad to sort herself out.'
Ms Gibson could face a criminal charge of wilfully neglecting the child. Civil proceedings could also be launched, leading to a possible care or supervision order.
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