I guess "God Save the Queen" (or King, depending on whether it's a bloke on the throne!) doesn't really need any intro:
http://en.wikipedia.org/wiki/God_Save_the_Queen
I think everybody knows what it sounds like......
England mainly uses "God Save the Queen", but "Jerusalem" is gaining popularity:
http://www.nationalanthems.info/eng!jeru.htm
Northern Ireland uses "Danny Boy/Londonderry Air":
http://www.nationalanthems.info/nie.htm
Wales uses "Hen Wlad fy Nhadau", also known as "Land of my Fathers" in English:
http://www.nationalanthems.info/wal.htm
Last, but not least, Scotland has "Flower of Scotland":
http://www.nationalanthems.info/sco.htm
I'm going to be a bit controversial here, but although "Flower of Scotland" is stirring enough, I can't say I particularly like it, and I do think it's a bit of a dirge. It's also been described as a "grudge set to music", which is arguably true.
I'd rather something a bit happier and with a snappy tempo had been chosen, like "Scotland the Brave"!
Mike.