text: The Duchess of Cambridge is already up to four days overdue with her second child - and her labour could now be induced this week, it was claimed today. The 33-year-old royal’s baby is expected before the end of April - with the due date initially reported as yesterday, but later claimed to actually be as early as Wednesday last week. Either way Kate - who plans to give birth at St Mary's Hospital in Paddington, central London - is now overdue and may have already spoken to doctors about the possibility of being induced. Scroll down for video . Previous royal birth: The Duke and Duchess of Cambridge leave the Lindo Wing of St Mary's Hospital in Paddington, central London, in a proud moment with their newborn  son Prince George in July 2013 . Due date: Preparations have been made outside the Lindo Wing of the hospital (pictured yesterday) for the huge crowds expected to welcome the royal birth - with the Duchess said to be up to four days overdue . A source, whose children were born at the hospital’s exclusive Lindo Wing, told Daily Telegraph reporter Gordon Rayner: ‘The doctors don’t normally wait for more than a week. ‘They will probably already have been in touch with Kate, and talked about which day which suit her best to go in and be induced if the baby doesn’t arrive in the next couple of days.’ A Kensington Palace source said last week: 'We haven't ever confirmed a due date.'  Prince George was reportedly born three days late when he arrived at the hospital in July 2013. The joint favourite dates for the royal baby to be born are tomorrow and Tuesday at 6/1 - with Wednesday priced at 7/1 and Thursday 8/1, according to MailOnline's official betting partner Coral. The bookmaker is also offering evens on a morning birth, 3/1 on the baby arriving in the afternoon and 2/1 on it being in the evening – while Alice (5/4) and Charlotte (5/1) are the favourite names. Royal fan: Terry Hutt (right) waits last week for the Duke and Duchess of Cambridge's second child to be born . Cute: Prince William and Kate pose with their son Prince George at the National History Museum in London . But some punters might look further ahead for their bets - if they believe those who say labour is influenced by the lunar cycle and the arrival of a full moon. The next full moon is on May 4. The idea is the moon's gravitational pull affects the amniotic fluid in the same way it affects water in the sea and rivers. When Kate gave birth  on July 22, 2013, it was the day of a new full moon. Meanwhile Prime Minister David Cameron has defended William and Kate for opting to use private health services rather than the NHS. Asked if he was disappointed the Royal Family did not use the NHS, Mr Cameron told Sky News today: ‘I think it's a total matter of choice for people - what they use and where they have their babies. All I hope and pray for is there'll be happy, healthy news for that wonderful couple and for the whole country.’ Around one in five deliveries in the UK is assisted. A Danish study in February suggested inducing women at 37 weeks can lower the chance of a baby dying or developing a serious health condition.
target: Due date believed to have been between last Wednesday and yesterday .
  Kate, 33, plans to give birth at St Mary's Hospital in Paddington, London .
  She may have already spoken to doctors about option of being induced .
  Bookmaker's 6/1 joint favourite for birth date is tomorrow and Tuesday .