Chocs - no one, to my knowledge, has ever estimated the number of 'illegal immigrants' that will come to the UK.
You're not, by any chance, confusing the issue of the estimates of EU citizens who would come to work in the UK (legally) after their countries joined the EU?
Quite a few Spaniards and French people objected to Brits buying up holiday homes and pushing up prices of real estate (and indeed causing a bubble in Spain) - and come to think of it, Welsh people weren't too keen on English people buying up second homes either, but that's another story.
Illegal immigrants actually tend to be the ones working in the menial jobs and actually contributing to the economy. Legal immigrants tend to contribute a lot more to the economy - as do those who came in from EU countries of Eastern Europe. The shortage of resources in local areas stemmed primarily from a lack of planning and a lack of revenue from central government to the local authorities.
And, as I pointed out before, the vast majority of illegal immigrants are Aussies and South Africans. The perverse thing is that over in Australia, there are thousands of illegal Brit immigrants there too (just look up the stats for over-stayers).
But hey, perhaps it is only the minority that look beyond the Daily Mail headlines?

At least I give Enoch Powell credit - his views weren't disguised behind euphemisms.
Cheers,
Shafique