The punts include stakes on what date it will be born and whether the tot will be a boy or a girl.
And bookies are on course to make hundreds of thousands of pounds more profit if, as feared, the Duchess of Cambridge does not deliver until August.
Medics at private St Mary’s Hospital in west London could wait up to two weeks before inducing the royal.
Jessica Bridge of Ladbrokes said: “We’d love it if Kate and Wills have completely pulled the wool over our eyes and are actually expecting a late July/early August baby.
“All the media thought the birth would be earlier, so that’s where all the money went.”
Ladbrokes, who have so far taken £25,000 in bets, said its biggest single wager came from a punter in Wiltshire who lost £1,000 on the baby being born last Wednesday, at odds of 3-1.
A flurry of bets have been made on the baby being a boy.
They came after Kate, 31, sparked rumours she is having a lad after snapping up blue curtains.
The Duchess of Cambridge was spotted choosing a £45-a-metre fabric in the traditionally masculine colour at a shop in Chelsea, west London.