A new "continental partnership" should be forged in the wake of the Brexit vote, which would allow the UK to remain in the single market while giving Theresa May the chance to introduce restrictions on free movement, according to a top EU think tank. The "tough" proposal is part of a new paper published by the Brussels-based Bruegel group.
The aim of the plan is to keep the UK close to the EU, with partnership of goods, services, capital mobility and security as well as a new system of inter-governmental decision making.
"This results in a Europe with an inner circle, the EU, with deep and political integration, and an outer circle with less integration," the paper said.
"Over the long-run this could also serve as a vision for structuring relations with Turkey, Ukraine and other countries."
But the proposal to allow the UK to have restrictions on labour movement is the most controversial.
The free movement of people is a fundamental principle for the EU and the union's leaders, including European Council president Donald Tusk, have warned that Britain cannot have "single market a la carte".
"Our proposal is driven by the firm belief that neither the EU and its member states nor the UK have an interest in an escalation of tensions or costly disengagement following Brexit," the Bruegel paper added.
"Neither the UK nor the continuing members of the EU can escape their geographical interdependencies. Both have a stake in economic and political stability in Europe.
"Today's volatile and dangerous world requires its nations to collaborate to confront new and multiple challenges. The longer-run prospect of a future world in which Europe is only one amongst many powerful regions demands the same."
However, concerns over immigration played a major in the Vote Leave campaign in the run up to the EU referendum. The group threw its support behind an Australian-style visa points system, which would restrict the number of EU citizens coming to the UK.
The most recent official figures showed net migration to Britain had dipped slightly to 327,000 in the year to March 2016, down by 9,000 compared to the year before. The data means the UK government had failed to meet its "tens of thousands" immigration target yet again.
Meanwhile, May faces increasing pressure over her Brexit plans and when she plans to trigger Article 50 of the Lisbon Treaty, the mechanism to signal the UK's split from the EU. Former Conservative leader and Leave campaigner Iain Duncan Smith has said it could be triggered in early 2017.