It had previously been reported that at 24, Cressida, a dance student who is a graduate of Leeds University, felt too young to settle down. She was also said to be unsure about marrying into one of the world's most high profile families.
But now the 29-year-old Prince seems to have won her round.
Prince Harry seems to have persuaded his girlfriend to consider marriage
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A source told HELLO! magazine that the couple are "very compatible" and "share the same sense of fun and adventure". "No one would be surprised at all if they married," added the insider.
Harry has been smitten ever since he was introduced to the young beauty by his cousin Princess Eugenie 18 months ago. When the helicopter pilot Prince was posted to Afghanistan last year, he kept in constant touch by phone.
During that tour of duty, he spoke about how difficult it would be to find a girl willing to take on his position and lifestyle – which was reportedly one of the problems with his former love Chelsy Davy.
Cressida is close to the Prince's cousin Eugenie and shares his sense of fun
Cressida, who is the daughter of Lady Mary-Gaye Curzon and her ex-husband Jeffrey Bonas, has long been on the fringes of royal circles.
Last year her half-sister Isabella Anstruther-Gough-Calthorpe married Richard Branson's son in a beautiful wedding at the businessman's private game reserve in the South African bush. Along with his sister Holly, Sam Branson is close to the young royals.
Her half brother Jacobi Anstruther-Gough-Calthorpe is a polo player said to count Prince William among his friends.
For more inside information on what makes the pair perfect for one another see this week's HELLO! magazine, issue 1298.