Just an update if anyone's still looking...
My dad had mentioned at the weekend he thought it sounded like a piece of classical music, but rearranged so I was about to check that when I got this email from Fiat....
Thank you for contacting the Fiat Information Centre.
In relation to the query you had regarding the Bravo advert music, it may sounds like Swan Lake but it's not.
It's a soundtrack, by Pete Diggens, bespoke composed for the Bravo ad.
Best regards, Fiat Information Centre
So there you go!