Cameron was travelling on the London Underground as it was quicker than going by car and during the journey he complimented a young mother on her baby.
But Sanyogita Mayer, 27, was clueless about him.Daily Mail said that Mayer was travelling with her husband Yanko, 31, and their three-month-old daughter Sayama when Cameron met them.
"We were on our way to go shopping. This man got on at Westminster and came past me and asked: "Is it your baby?"
"I said 'yes', and he said: 'Your baby is really beautiful'," Mayer, who has recently moved to England from India, was quoted as saying.
Mayer thanked Cameron who stood near her.A baffled Mayer then asked her husband: “Who is this man complimenting my baby?”
"When he (Yanko) told me it was the prime minister I told him to stop joking with me.
"But my husband insisted so I went up to Cameron and I said: `Excuse me, are you the prime minister?'
When Cameron replied in the affirmative, she started laughing and apologised for having asked him the question.
Mayer told the prime minister that politicians in India would never travel by public transport.
"He (Cameron) told me he had a very busy schedule and it was quicker for him to travel by train than go by road," she said.
Cameron who was accompanied by a bodyguard spoke to her about India.
The prime minister said that he had travelled by train in Delhi, gone to Mumbai and received a signed cricket ball from Indian cricketer Sachin Tendulkar.
"I was so surprised that a man like him would travel on the Tube and I was very struck by how down to earth he seemed," said Mayer.