Jerusalem's a good choice because 1, most importantly it's a great, short piece of music with a good crescendo.
2 Because it's about questioning the direction of the country and devoting yourself to making it better. The whole premise is Milton questioning if the England he sees with "Black Satanic Mills" of the industrial revolutioncould really be the place Jesus supposedly visited, and then concluding that he shouldn't rest until he's built Utopia in England.
It's obviously set against the backdrop of religion but the message is a good one. The idea Jesus visited England is more of an English folk story than religious anyway because it's not endorsed by any religion (or History).
You can't really just draw up some secular anthem, the song that replaces the dirge that is GSTQ needs to have massive popular backing and be known by most people.