Yasmin Gibson, 32, made two telephone calls to a woman neighbour who had previously looked after her daughter, Gemma, at her flat in Hammersmith, west London.
The plight of the young girl, who is now being looked after by the social services, was revealed on Friday.
A Scotland Yard spokeswoman said: 'She (Ms Gibson) contacted the elderly neighbour who looked after her and who had alerted the social services.
'But we are not prepared to discuss what Ms Gibson said to the woman. We still believe she is in Spain and efforts are being made to trace her.'
She added there was no indication as to when the mother would be returning to Britain.
Police in Malaga, where Ms Gibson is thought to be on holiday, said they were unlikely to have much difficulty tracing her. They said they had not been able to make many inquiries yet because they were dealing with Spain's biggest-ever heroin haul.
They are expected to concentrate a search for Ms Gibson on the coastal area between Fuenguirola and Marbella, where many British expatriates own homes and bars.
One of the first places to look would be the hills around the village of Coin, where the BBC series Eldorado is filmed.
'Judging by the pictures we've seen in the press, she shouldn't be hard to find,' said one officer.
Foreigners are still carefully vetted in Spain. If Ms Gibson
registered in a hotel or boarding house under her own name, or showed her passport anywhere in order to change money, she is almost certain to be found quickly.
Ms Gibson may have arranged a childminder for Gemma before leaving for Spain, according to the west London council in whose care the girl was placed after she was made a ward of court.
Hammersmith and Fulham social workers yesterday were trying to establish whether there had been a misunderstanding about child-minding.
'In the past, we understand that the mother had made arrangements with a neighbour,' a spokeswoman said.
'For some reason on this occasion the neighbour did not think that she was meant to be looking after the child.'
It is not known how long
Gemma had been alone in the two-bedroom flat. The caretaker who alerted police said the youngster was 'only alone for about a day and wasn't really at risk'.