In a perfect world Dotty but it goes on.
One of the places I go for coffee a lot has a lot of Polish workers and they are polite, friendly, hard workers, I'd rather employ many of them than some British slackers. It's about employing good quality staff regardless of where they come from.
Many of the hospital staff doing the cleaning work and such seem to be immigrants. I imagine for a similar reason.
I live in a very multicultural area and the load of people from other ethnic minorities (who knows if they are immigrants or not) who get the 6am bus into the city that I do each morning must be going somewhere - aka, they work, they contribute and support themselves and their families. Many have cleaning jobs at places like the universities or hospital.
I'm sure that there are a number who don't but then the same thing applies to a lot of British people who just can't be bothered to work and would rather live on benefits.
I went to help run a youth camp in Romania years ago and a fair few of the kids, now adults, have moved away to places like here and all the ones I know of work and support themselves. Trouble is, people like a group we have locally who harass people in town for money (usually with babies and children involved and literally grabbing and following people) give other hard working immigrants a bad name.