Brussels will propose centralising control of asylum claims in the EU as part of a radical overhaul of refugee policy in response to Europe’s biggest migration crisis since the second world war.

News of the sweeping initiative from the European Commission risks inflaming Eurosceptic sentiment in Britain ahead of the EU referendum in June, with critics likely to see it as a further power grab by Brussels.

The commission has gone to great pains to hold back new rules that could alienate British voters. But the commission’s decision to present its asylum initiative ahead of a summit of EU leaders on March 17 is a measure of how concerns over migration have trumped concerns about Brexit in Brussels — a reality that UK officials faced repeatedly during Mr Cameron’s “new settlement” negotiation last year.

The commission is examining ways to overhaul the bloc’s rules on who is responsible for asylum claims after the system collapsed amid an influx of 1.3m applications in 2015.

Under the current system, known as the “Dublin regulation”, refugees have to claim asylum in the first EU country they enter. That heaps pressure on the countries at the EU’s borders, such as Greece and Italy, but shields others that are further away.

The Dublin rule fell into disarray when Angela Merkel opted not to enforce it last autumn, triggering a rush of people trying to reach Germany.

According to draft reform options seen by the Financial Times, responsibility for all asylum claims could be shifted to the European Asylum Support Office.

This offers advice to national governments but would be turned into a federal agency responsible for claims. If Brussels pressed ahead with this option it would mark another transfer of sovereignty to the EU and ultimately require treaty change.

The UK has an “opt-out” on matters of justice and home affairs and would not be forced to join any new system.

But the plan will prompt unease just as Britain is trying to resist separate changes to the Dublin regulation, which has allowed the British to transfer 12,000 asylum seekers to other EU countries since 2003. The UK could lose that facility under the overhaul if it decides to opt out of the new system.

Justine Greening, development secretary, has warned that London would be “concerned and strongly against” any such plans if they ended the “initial country status” approach.

The commission will present two options. The first is to fundamentally reshape the bloc’s system and would result in all asylum seekers being shared out across the EU on a quota basis, regardless of where they first arrived. The other would keep the status quo — but with asylum seekers shared out on a quota basis if a country is overwhelmed by a sudden influx.

Efforts to share out refugees across the EU have stalled in recent months, after months of diplomatic squabbling between Berlin and its eastern neighbours, as well as technical problems. A flagship scheme to relocate 160,000 refugees from Italy and Greece has so far resulted in fewer than 700 being moved.

While Britain has taken relatively few refugees from Syria or Iraq, immigration is taking centre stage in the increasingly febrile EU referendum debate. Net migration is now higher than 300,000 a year, in part because of EU membership.

Some “In” campaigners fear the consequences of holding the referendum in late June amid images of southern Europe being overwhelmed by a surge of refugees from the Middle East.