The royal made the revelation during the couple's visit to King's Hospital in Camberwell, where Camilla was born to Major Bruce Shand and his wife, the Hon Rosalind Shand on 17 July, 1947.
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She was delivered by the Queen's obstetrician, Sir William Gilliat, who worked at the hospital. A year later, on 14 November, 1948, he delivered Charles in Buckingham Palace.
"My darling wife was born here, but amazingly we had the same gynecologist and nurse," the Prince told fascinated staff.
Camilla met Gemma Cherry and her 11 week-old daughter Ameilie
Grandparents Charles and Camilla visited the neonatal ward during their tour of the hospital, where the Duchess proved to be a natural at cheering up the young children.
Amy Bernadout, 19, whose five-month-old son Jessie is a patient at the hospital, told reporters, "Camilla was fantastic. She had Jessie in fits of giggles and was so good with him, pulling funny faces to make him laugh.
"She's a gran herself, so she's obviously good with babies."
Camilla and Charles visited the neo-natal intensive care ward in King's hospital
Camilla, who was presented with a teddybear decorated with the words 'I'm a King's baby', has five grandchildren, including twin boys. She took a particular interest in the premature babies still in their incubators.
Nurse Ruth Finlay, 23, said, "The duchess was quite overwhelmed seeing such tiny babies. I was feeing one of our premature twins and she said her daughter had had identical twins too.
The couple also made time to sit down and have a chat with Jesse Crowden, 88
The royal couple also spent time with other patients in the hospital, including 88-year-old Jesse Crowden.
Before they left, Charles told staff, "The work you do here is fantastic, particularly having seen the neonatal unit and elderly wing - even more significant with our advancing years!"