Elizabeth has overtaken Diana as the favourite royal baby name for a girl in some quarters.
Coral have slashed the odds after a flurry of bets that the Duke and Duchess of Sussex will choose to honour the Queen if they welcome a daughter.
Elizabeth is now 6-1, down from 16-1, while Diana is the second favourite at 8-1, alongside Victoria.
Harry Aitkenhead of Coral said: “We’ve been bowled over by this gamble and out of absolutely nowhere Elizabeth is the new favourite to be the name of Harry and Meghan’s first child.
“Royal punters are betting in their droves and they’re clearly convinced that they know a baby Elizabeth is on the way.”
Paddy Power still has Diana, which Harry could choose in tribute to his late mother, as the top-rated name at 3-1, followed by Grace at 7-1 or Charles for a boy at 13-1, and Victoria, James, Alice and Edward at 14-1.
Punters are predicting that Harry and Meghan’s first child, due this month, will be a girl.
The odds are 10-1 the baby will arrive on the Queen’s birthday on April 21 and 4-1 that Meghan will give birth to twins.