Let me just add my two pennies worth. I'm not an immigrant in the UK, although I had been thinking about going there for a couple of years, but that was before the crisis. I live in the Czech Republic and want to give you a different perspective, seeing it as a person from this Eastern Eurepean country.
In 1990's Czech people were drunk with freedom and possibilities and many of them wished to go abroad to the afore forbidden West to work and learn the language. However, it was impossible to do it legally. The only legal possibility was to come as au pairs. Therefore many people who wanted to work, did the worst kind of jobs because they were the only jobs they could get illegally. Law graduates worked as au pairs and engineers worked as cleaners because even though the work was something they would have never done at home, it paid many times more than their professional jobs back home. They were risking deportation etc.
During the same period of time, loads of illegal immigrants from Russia, Ucraine and other countries came to our country for a change. And they still do come to do the same kind of jobs the Czech used to do or still do in the UK. So it is in fact a kind of a vicious circle and we are dealing with many similar problems like any other EU country, but on a smaller scale than the UK, of course.
However, many of the Czech work-immigrants came back home later or they became successful in their profession (especially in construction) and stayed in the UK. Only a few stayed for good because they got married or have children with a UK citizen and therefore decided to make the UK their new home. BTW. NHS is one of the factors why they keep coming back. Many Czechs living in the UK greatly complain about it and prefer the Czech Health system. To give you an example, pregnant women in the CZ routinely have several ultrasound scans during their pregnancy and several other tests like diabetes, genetic disease scans etc. Whereas this is virtually non-existent in the UK, as you might probably confirm. (I'm not 100% sure, correct me, if I'm wrong.)
Finally, in 2007 we were allowed to come to work without any restrictions. This didn't make all the Czechs suddenly change their mind, pack up and move to the UK. Not all people (now I mean it in general for all countries and people) are actually able to move for work because most people are very much attached to their place of birth and their families and friends at home. So in 2007, it only made things easier, more transparent and legal. Besides, as someone above mentioned, most of the people who wanted to have foreign work or study experience or move there because they simply like the country are already there and there was no disastrous wave of Czech, Polish etc. immigrants in 2007 as the media in the UK had believed just like now.
In my opinion, these anti-immigrant feelings are caused by the economic crisis that Europe is still undergoing and the inability of governments in the EU to do something about it. Unemployment is rising everywhere and people have to watch their budgets more carefully than they used to do. The immigrants that were originally so useful are suddenly seen as thieves of jobs that no one wanted to do ten years ago. In my country, people haven't started to blame the immigrants yet, it's the unemployed now, but I'm sure it's going to be the same as in the UK sooner or later because immigrants keep coming and jobs are scarcer and scarcer.