Britain has seen two Marys on the throne - Mary I, known as Bloody Mary for her persecution of Protestants, and Mary II, who ruled jointly as monarch with her Dutch husband William III.
The Duchess of Cambridge at an engagement in Essex last week. Photo / Getty Images
The last example of a great-granddaughter of a still-serving sovereign born on the male line was Princess Mary, who was born in 1897 and was George VI's sister.
Jessica Bridge, of Ladbrokes, said: "We can't quite put our finger on the link between Mary and the North West, but the overwhelming support means we have a new favourite in the royal baby name market."
She added: "Punters are convinced the Duke and Duchess are expecting another little girl, and obviously it would be a lovely touch to honour Her Majesty's grandmother, but it will be interesting to see if any boys' names are backed over the coming weeks before the birth."
Kate and William's third baby is due in May. Photo / Getty Images
Mary has steadily fallen out of fashion over the last century.
In 1904, it was the most popular name given to girls in England and Wales.
But it not longer appears in the list of top 100 girls' names in England and Wales, according to the Office for National Statistics.
Ladbrokes has Mary at odds of 7-1, followed by Alice and Victoria at 8-1 and Alexandra at 16-1, while Albert or Arthur are 12-1 for a baby boy.
