Why wouldn't they stay, legally or ilegally, in the equally rich Germany, France, Netherlands, Belgium, Sweden, Finland, Austria? All of which are closer to the origin countries than the UK.
Or why wouldn't they go in the slightly-less-richer, but culturally closer Spain or Italy? Especially since the weather is much nicer over there :)
As a British guy in Finland I can say that the reason many people moved to the UK was because of the perception of easy work, easy integration, and good practices.
Those things might exist in other countries, I don't know of them personally, but I do know that moving to Finland is non-trivial. The language is hard, and unless you speak it you've only got unskilled jobs to find - with high competition. Gaining residency pretty much necessitates having a job too, which makes it all a bit circular.
I'm settled here for the foreseeable future, although I have to wait another couple of years before I qualify for citizenship.
English language, maybe? Obviously a lot of those other countries have very high numbers of English speakers, but most good jobs still require you to speak the native language.
Or why wouldn't they go in the slightly-less-richer, but culturally closer Spain or Italy? Especially since the weather is much nicer over there :)