most immigrants come here because their home country had a much lower standard of living - aside from the opportunity. So I am surprised that you took so much trouble; surely Britain has an equivalent standard of living?
I can't figure out whether the people who run immigration in most countries are complete morons on their own, or if their political masters have significant influence in the stupidity of the system. My own personal example (well, one): when I got married in Italy, I had to swear, in front of a (busy) judge, with two witnesses, that no, I was not actually married elsewhere.
I don't think there would be any huge effects if things were basically opened up between wealthy countries... a few would go here from there, and vice versa, and things would balance out. But it is increasingly difficult. Bleagh!
For starters. You couldn't realistically completely open, Holland, say, to immigration from India and China without some adverse consequences. Between rich countries, people would likely flow back and forth enough to balance things out.