It is open for debate if the percentage is higher than in the original population and no, they don't suck up 'huge amounts of public money'.
The problem lies more with the economic immigrants abusing the asylum systems to gain entry.
The immigrant problem the likes of Boris complains about (other EU citizen) is a non-problem, mainly caused by too low wages, too little housing and too generous benefits in the UK, all problems caused and maintained by his Tory government, not Brussels.
As the UK (the über-Tory Maggie Thatcher!) had signed up to the EU including the free movement of capital and persons these people should not even be called immigrants.
Although I'm right now in the UK I am living in The Netherlands and I can tell you the people he is complaining about are net contributors to the UK economy, not leaching on it's benefits, similar can be said about the Hispanic immigrants to the US that Trump rallies against, like without them the average American lawn would be a wilderness.
Those that Wilders and le Pen are afraid of (immigrants from Africa and the Middle East) need better chances at integration, including more pressure on them to actually integrate or else be send home.
Another EU problem is when we tore down the internal borders we conveniently 'forgot' to transfer part of the thus generated monies to a joint border protection on the outside. Brussels would like such but the individual member states are reluctant.