They think that if you emigrate to the UK and are not British citizens that you shouldn't be entitled to out-of-work benefits, housing benefit or social housing, free healthcare (should be paid for by country you normally reside in) or free education until you have paid taxes here for a certain number of years.
Why count it in number of years rather than in amount of tax contributions? A high earning foreigner - of which there are many, particularly in London - may well pay more taxes in a few months than some British born and bred have ever paid. And once other countries take retaliative action we will be deluged with British ex-pats scurrying home, their tails between their legs, asking for housing, healthcare and education.
If you can't afford private housing, or to HE or privately school your children for those years then you shouldn't chose to move here.
Seriously? You want to set the income bar so high that people have to show themselves able to find 20k+ per year for private education before coming here? You do know that this would utterly destroy our universities, our scientific research, our engineering companies, our financial industry etc etc. All of these recruit highly skilled foreign workers, generally on decent salaries, but not necessarily salaries which suffice to pay school fees.
Didn't Labour under Gordon Brown remove a lot of school places, despite the evidence that more places would be needed a few years down the line? Why aren't people angrier about half-full failing academies and free schools in the wrong areas draining the education budget?