In my opinion, the feelings range from mild resentment to simmering dislike.
Is there the same cultural divide in England as there is in the U.S.: the people being overwhelmingly in favor of limiting immigration, while the politicians allow it to go on?
Yes.
My opinion: this is what socialized medicine has wrought. The Baby Boomers never bothered to reproduce and to replace their numbers, so their retirement would be a financial disaster for any nation that didn't allow in untold numbers of immigrants to pay for the old folks' medical care.
Not really. What happens is this - as societies become more affluent, birth rates generally go down. It is becoming more and more expensive to raise a child as we become wealthier (I know that sounds odd, but a child 30 years ago didn't need an XBox) and birth control is more readily available.
Socialised medicine hasn't helped, but it is a function of affluence I believe.
Regards, Ivan