Sanyogita Mayer, 27, was travelling on the tube with her husband Yanko and their daughter 16-week-old Sayama in October 2011.
The family were travelling on the Eastbound Jubilee line train at about 11am when David Cameron got on at Westminister and complimented Sanyogita on her beautiful baby.
Sanyogita had no idea who he was and said to her husband in front of Cameron: 'Who is this man telling me my baby is beautiful?'
Yanko told her he was the Prime Minister.
Sanyogita thought it was a joke and asked Cameron who he really was. He insisted that he was indeed the PM.
More top news
Terry Perkins and Daniel Jones described as "premier league criminals" are alleged to have broken into Chatila jewellers in Old Bond Street.
Kingston police station had to be partially evacuated after the two shells, designed to hold explosive ammunition, were handed in.
The controversial TfL package includes a requirement that drivers undertake tests in reading and writing basic English.