Cameron's show off newborn Florence outside No. 10

The newborn appeared unfazed by the numerousf photographers and camera crews on the other side of the street.

Asked how many nappies he had changed, the Prime Minister joked: "Hundreds."

Another journalist asked: "Has Nick Clegg changed any nappies yet?" Cameron replied: "That's next."

The baby was wearing a white shawl crocheted by a member of the public who sent it in to congratulate the couple on the birth. The woman, Jane Fraser-Cross, from Sutton Coldfield, Birmingham, is a local fundraiser and grandmother of six.

Mrs Cameron was wearing an orange dress made by a local dressmaker in which she has been pictured several times before. She also wore a blue skirt and heeled shoes by LK Bennett.

Asked if the baby was keeping them awake, she smiled and replied: "Yes." Mr Cameron bent to kiss the baby on the head and she opened her eyes briefly.

Florence was born at the Royal Cornwall Hospital in Truro last Tuesday, weighing 6lb 1oz. She was not expected until this month, but caught the family by surprise while they were on holiday. Her middle name, Endellion, refers to the village of St Endellion on the north Cornish coast, near where the Camerons were staying.

The Camerons are also parents to Nancy, six, and Arthur Elwen, four. Mr and Mrs Cameron lost their other son, Ivan, who suffered from cerebral palsy and severe epilepsy, when he died aged six last year.