The Duchess, who plans to give birth at the exclusive Lindo Wing at St Mary's Hospital in Paddington, London, revealed last month that her baby was due to arrive mid to late April.
The Duke and Duchess of Cambridge's second child - fourth in line to the throne, the Queen's fifth great-grandchild and a younger brother or sister for Prince George - is due any day now amid reports he or she may even be overdue.
Fewer than one in 20 women give birth on their due date. On the NHS, induction is offered to women who go two weeks overdue.
The chance of the baby arriving on the same day as the General Election - May 7 - is put at 16/1.
Bookmaker Paddy Power said one customer has placed a £5,000 bet on a May Day birth at odds of 9/1 and stands to win £50,000 if the gamble proves correct and Kate delivers a son or daughter on Friday.
The Duchess of Cambridge visited the Brookhill Children's Centre in Woolwich
The 33-year-old wore a blue and white Asos maternity dress with black shoes and chatted with families and volunteers.
Prince Harry is on his way back to Australia, meaning he will miss the birth of the royal birth.
Harry is returning overseas to spend time with Australian Army units in Perth and Sydney before he embarks on an official tour of New Zealand from May 9 to May 16.
Volunteer Christie Osborne, 49, was among those the Duchess sat and spoke to at the coffee morning in March.
She said: "I told her she is beautiful and that she's got a tiny little bump. I asked when her baby is due and she said mid-to-end of April."
Kate also received a goodie bag for Prince George embroidered with his name and a bouquet of flowers.
Kate is due to give birth between the middle and end of April
Marvellous Nyanhi and her son Tinashe handed over the presents, which included an Elmer the Elephant book, a potty training booklet and a colour-sorting clock.
The centre is run by Home Start charity, which recruits and trains volunteers to support parents with at least one child under the age of five.
The charity helps more than 29,000 families each year who are dealing with issues including isolation, mental health problems, bereavement, multiple births, illness or disability.
It runs four of Greenwich council's 24 children's centres which offer services including early-years education, childcare, family health services and employment and training advice for parents.
POSSIBLE ROYAL BABY NAMES