No, they won't

Cameron was interviewed today trying to appear tough on immigration, which is admittedly what we want to hear, though sadly I suspect words and actions will not match up.
Telegraph.

In an interview with the Daily Express, the Prime Minister said he wants to ban migrants from being able to automatically receive legal aid in cases involving benefits, housing and other civil claims. Mr Cameron this month said he want to completely overhaul the benefits system for migrants after saying that he believes the current system does not pass the “simple common sense test”. The Prime Minister said he has asked Chris Grayling, the Justice Secretary, to create a new “residency test” designed to ensure migrants are not given instant access to legal aid in civil court cases. Mr Cameron said: “We’re a fair country and a welcoming country, but not a soft touch. Let’s make sure that ours is the toughest country instead of the softest.” “I think there is more we can do,” he added. “One of the aspects that we are reaching fairly early conclusion on is that we can no longer grant legal aid to non-UK nationals or for civil cases, people who are facing housing cases or benefit cases.

The problem is, the non UK nationals he's talking about are mostly EU citizens and we can't (under EU law) treat them any different to our own otherwise they go to the courts and our judges turn around and tell the government to do it anyway.
The only way to reclaim control over our borders is to tell the EU to take a running jump and there's no way in hell Cameron will do this as he's in love with the damned corrupt edifice and believes we should stay in no matter how badly they treat us.
It's always the same with him, he says things he knows the EU will not let him do, it sounds good on tv but in reality he simply does not have the power to overrule Brussels directives nor the political will to even try. The man is simply Brussels's puppet here to do what they want and ensure ever closer union despite a lot of people here being hell bent on stopping this and removing ourselves from the EU totally. That's why he talks tough on certain issues, that and attempting to get re-elected one day to carry on with the good work of the EU, though as Millipede E is a staunch EU supporter that's not too important to the bureaucrats of Brussels's.
So, just another interview spouting hot air on a subject he can't do anything about.
Nothing new then.