In absolute numbers of immigrants, though, Britain is 5th in the world - 3rd, if you exclude Russia and Saudi Arabia on the grounds that they're hellholes that nobody in their right mind would want to move to without powerful independent incentives.
I have no first-hand experience living Saudi Arabia, so I can't comment on it. Russia, on the other hand, can be quite pleasant, provided that you make the effort of learning the language, and accept that the culture and the way things work will not be the same you are used to. It is not to everybody's liking, of course. On the whole, I would not want to live in Russia, and certainly not in Moscow (although I have no doubt I would make a comfortable living there) - but my wife, for example, likes going to Russia very much.
As far as net migration to Russia is concerned, it used to be mostly ethnic Russians escaping the post-Soviet chaos of the central-Asian stans - so one should really classify these migrants as refugees. That time is over; the present net migration is mostly economic. In the European part of the country, it still comes mostly from the ex-Soviet space (mostly the same stans, plus Ukraine); this makes perfect sense: the biggest barrier for migration to Russia is the language, and these countries have a long (if not entirely voluntary) tradition of learning it - not unlike the Commonwealth, if you think about it.