At least we think we do.
According to the Daily Mail, Kate and Wills were at a barbeque with their mates over the weekend and someone overheard them mumbling about dates and babies and so of course it's confirmed when the royal baby is expected to make its grand entrance. We expect there'll be fanfare and confetti, and all the animals will gather like at the start of The Lion King.
Anyway, said date is July 13th, which happens to fall bang in the middle of a Coronation Festival marking 60 years since Queen Liz Two sat in the throne, which is both problematic and perfect timing; problematic because obviously no one wants to see amniotic fluid falling in public and therefore Kate's going to have to be kept away but also perfect because HELLO PRESS when that sprog pops out. One would almost think one had planned it. *cough conspiracy theory cough*
Anyway the big mouth who blabbed about the due date had this to say 'Some of Kate and William's closest pals were at a barbecue hosted by a family friend of the royals recently. They were all discussing the fact that Kate's baby is due to be born on July 13. Everyone was very excited'. So Kate's not keeping it so secret then?
The official line from Royal HQ is that there is no confirmed date and that anything other than 'July' is imaginary with a rep saying 'We have only said that the duchess is due in July. Anything further would be speculation'.