I don't know if people want to become 'British', but it's certainly very popular to have a British Passport.
If you've travelled a lot, you'll find that the British Passport is like a golden ticket. Also, if you live and work abroad in places like the middle east, a British Passport entitles a child to a British education from the British Embassy . It also entitles them to reside in the UK if they wish to in the future (and enjoy all the benefits while their at it).
I live and work abroad (in Qatar) and it really angered me to find out that there are lots of kids living here born to foreign parents (whether it be Australian, Swedish, Iranian - whatever) who have British Passports because their parents once lived in the UK for long enough to become a British citizen. Currently, if one of the child's parents has a British passport, the child can apply for one as well.
Believe me, as much as the majority moan about the UK, the UK is where everyone in else in world wants to be. It's a bit rough back there at the moment , but there is so much that is still Great about Britain and it will recover, so be proud to be British and don't put it down.
And by the way, I know I'm not living there or paying UK tax at the moment, but I WILL BE BACK to spend all the money I've earned in Qatar in my own country.