Do not under estimate how difficult it is to get into corporate flying.
No, you don't need a degree. You do need contacts and (usually) a lot more experience than the airlines request.
Whirlygig's hit the nail on the head. Get the licence that is appropriate where you can work.
You're a british citizen, therefore JAA/EASA lic is appropriate.
You'd need a visa for the US and Australia. So you can train there but may not be able to work.
If you're looking at Asia, then all the licences are appropriate as you'll convert them.