Duchess of Cambridge's touching note to bereaved mum

Kate the Duchess of Cambridge at the East Anglia's Children's Hospices (EACH) charity at the Norfolk Showground. Photo / AP

A bereaved mother says the Duchess of Cambridge wrote personally to console her following the death of her baby daughter.

Kate was attending a fundraising campaign launch for East Anglia's Children's Hospices when she met families who have benefited from the charity's work.

Among them was Leigh Smith, a 33-year-old physiotherapist from Norwich whose daughter Beatrice died from a rare heart condition after just 89 days.

She revealed how she wrote a letter to Kate outlining her story, only to receive a personal reply from the duchess.

"I was so surprised to receive a letter with such personal comments and signed by her," Smith said.

"It was a lovely gesture and helped me through a terrible time.

"I was touched that she had taken so much time to carefully read my letter and then to reply herself - it shows how much she cares.

"When I met her today she remembered the letter and said it was an honour to meet me.

"I was completely taken aback - for me it was an honour to meet her."

Beatrice would be due to turn one on Friday.

"I had mixed feelings about today because it's a difficult time but this is the most amazing way of celebrating her birthday and I hope Beatrice was looking down as I met Kate," Smith said.

The duchess braved the cold as she went without a coat and wore a red knee-length dress by Katherine Hooker and black sued stiletto pumps as she arrived at the Norfolk Showground on a frosty morning with temperatures of about three degrees.

There was just a hint of a baby bump as she met families, volunteers and staff before joining 700 guests for the appeal's launch.

- AAP