My advice to you is to do it in Canada. They make you jump through some hoops in UK. In England the Canadian would have to be there for 21 days, unless you head up to Scotland, but they require a ton of paperwork 8 weeks in advance. N Ireland is another option, but still has a lot of red tape.
In good ol' Canada, you go to the registry 3 days prior, get your license and you're good to go!
Not sure about Elvis though....that's Vegas, which would also be fun! Just make sure to take a ton of pictures for evidence, and keep receipts for things like rings, marriage commissioner, reception, etc.