Last week’s UK leaders debate included a long discussion about immigration.

UKIP’s Nigel Farage (pictured above in a variety of poses) declared “As members of the EU, what can we do to control immigration? Let me tell you — nothing”.

Other party leaders such as Prime Minister David Cameron, Deputy Prime Minister Nick Clegg and Prime-Ministerial-Hopeful Ed Miliband all emoted about what they saw as a problem of excessive immigration and gave various commitments as to how they would restrict access to welfare benefits for EU immigrants as a way to address this development.

For such an important issue, I found it striking how the debate revolved almost entirely around myths and misconceptions. Here are three important facts about UK immigration that should have been central to the debate but were not.

Fact 1: Most Immigration To The UK Is From Outside The EU

The idea that EU membership allows the UK no room to set its own immigration policy is blatantly false. A quick check of the official statistics from the Office for National Statistics shows net immigration from non-EU countries has always been larger than from the EU.

This means the UK has plenty of room to control immigration via limits on non-EU immigration. Indeed, non-EU immigration has generally been running at lower rates in recent years because the UK has introduced a points system and placed caps on the entry of various classes of people.

You can debate whether or not further restrictions of this kind (for example, further limiting the ability of UK universities to recruit fee-paying non-EU students) are a good idea. I don’t think they are but those who oppose high rates of immigration should spend more time focused on these issues than on blaming the EU.

Fact 2: Eastern European Immigrants Come For Work, Not Benefits

Of course, the chart above does show a big increase in net migration to the UK from the EU since 2004. This was the year eight Eastern European countries joined the EU. The UK decided at the time to allow full access for these EU citizens and there has been substantial immigration from these countries over the past decade. Indeed, Polish is now by some distance the most common non-British nationality for people residing in the UK.

So, to a large extent, the increase in EU-related immigration to the UK relates to Eastern Europeans moving to Britain. Cameron, Clegg and Miliband were all eager to counter Farage’s point that immigration from inside the EU could not be controlled. Each of them discussed their plans to cut down on welfare benefits for EU citizens coming to the UK as a way to reduce immigration from this source.

The theory behind this proposal appears to be that many people from Eastern Europe come to the UK because they can claim attractive social welfare benefits. The truth, however, is that immigrants from Eastern Europe come to the UK to work.

Look at the graph below (constructed from ONS statistics). As soon as people from Eastern Europe could come to the UK in 2004, they worked in far higher proportions than immigrants from other parts of the world. Indeed, people born in Eastern Europe have notably higher employment rates than those born in the UK. The idea that reducing eligibility for welfare benefits will have much impact on the presence of these people in the UK appears to be pure fantasy.