In a recent BBC news feature about Lampedusa, one Italian official described how a migrant implored her to make up a convincing asylum story for him. So they know they have to say the right things to get into the EU but some don't have the details down pat.
After hearing that, I think we should declare a moratorium on asylum claims and treat them all as economic migrants and tell new arrivals this is so because there are so many of them that we simply can't tell them apart any more.
I'm not sure if economic migrant status necessarily means instant deportation but we could have it such that they get an N.I. number in exchange for full disclosure of where they they've been told the job is (full follow-up if the same address crops up more than 10 times, say). No job details = sent back.
When the influx has returned to a manageable trickle, we can resume processing asylum claims. In the interim, we can deal with the current backlog of claims.
Can we cope with the population influx? In absolute terms, yes. But can we build a new city the size of Birmingham overnight? No. Can we expand 20,000 named UK settlements (hamlet and up) by 1 each? Yes, but probably not simultaneously. Can we force a migrant to settle in a rural backwater which is no better for their earning/career prospects than the village they left behind? No. They'll gravitate to the cities to "take the jobs" which our own rural poor have convinced themselves are too far away, or they don't have contacts in the city (and other excuses). Let's face it, if you're prepared to move a few thousand miles, what's another 300, at the end of the trip?