Let's start with the questions posed.
Most polls of this sort will give respondents a list of issues, preferably in randomised order, and ask them to identify the one/two/three most important issues. The issues from which to choose will vary somewhat over time as issues rise and fall, but many of them are fairly constant. Common issues include:
This is where the results get interesting.
Let's take the Eurobarometer (May 2013) results. First, let's look at the rankings for the question, 'What do you think are the two most important issues facing the UK at the moment?'
For nationally pressing issues, unemployment and immigration clearly rank as the top issues. But the picture looks distinctly different when we look at answers to the second question, 'And personally, what are the two most important issues you are facing at the moment?'
Suddenly, immigration comes in as eighth most important.
What does this mean? A lot of people think immigration is a pressing issue at the national level but isn't for them. This indicates that respondents are picking up on government rhetoric and mass media reports that frame immigration as a pressing problem, but in actuality, the vast majority of people are facing far more pressing issues. It's not possible for something to be a pressing national issue that is a pressing personal issue for so few people.
Thus, whilst we should respond to people's fears about immigration, we should take such polls with a very generous pinch of salt. Our response should be more about education with less focus on perceptions that aren't based on any evidence.