They may not see eye to eye on the big issues such as trade and migration, but Theresa May and EU leaders may be closer than you think to agreeing the terms and scope for a transition period.

If the latest reports are correct, the prime minister may be about to double her offer on the financial settlement to £38bn in order to unblock the talks before the December summit of EU leaders.

If she does, she has a realistic route to a deal on the transition. Indeed, the blueprint for a transition period that we would advocate as the most viable – where the UK gives up its membership but accepts EU laws lock, stock and barrel – is the one that they are actually edging towards.

A status quo transitional deal would buy Britain time – an invaluable resource

You just have to look at May’s Florence speech, in which she made clear that the UK seeks a transition where “access to one another’s markets should continue on current terms”, ie nothing changes. She even accepted that the framework for this period would be “the existing structure of EU rules and regulations”, with David Davis confirming in his speech last Thursday to German business leaders that the UK wants to remain in all EU regulatory agencies during the transition. Similarly, the EU has also indicated that it would accept a status quo transition, but this would require “existing union regulatory, budgetary, supervisory, judiciary and enforcement instruments and structures to apply”.

An extension of the EU acquis (the full body of EU law) to the UK, without EU membership, is the obvious choice for the post-Brexit transition. It’s comprehensive, meaning that very little changes on Brexit day. It’s relatively straightforward from a legal perspective, at least compared with other options, such as staying in the single market via the European Free Trade Association or an European Economic Area copycat agreement. Crucially, it’s politically feasible.

Of course, there would be bitter pills to swallow. What’s the point of leaving the EU if nothing changes aside from losing your seat at the table? However, May has already accepted free movement, budgetary contributions and a role for the European court of justice (ECJ) in the transition, and the government recognises that wasting time negotiating a bespoke transition is futile when the future relationship is the big prize. Why fill yourself up on the starter when the main course is still to come?

What would an extension of the EU acquis, without membership, actually mean? First, the whole body of EU law would continue to apply in the UK post-Brexit, meaning cooperation in many areas, such as trade and security, could carry on unchanged. Second, the UK would continue to accept the burdens and obligations of membership, despite losing its representation in the EU institutions. Third, it would enable the UK and the EU to continue sorting out their future relationship after withdrawal, with minimal disruption.

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However, there would be challenges. For example, the EU would insist on ECJ jurisdiction continuing, and the legal principles of supremacy and direct effect being upheld. It would also not accept bespoke, sectoral carve-outs in areas like fisheries and agriculture – much to Michael Gove’s dismay – due to the interwoven and cross-cutting nature of EU law. Finally, the issue of the UK’s status vis-a-vis the EU’s international agreements with third parties, including a whole series of free trade agreements like Ceta, would remain unresolved.

Despite this, an extension of the EU acquis, without membership, is much easier to sort out, both legally and politically, than every conceivable alternative transitional option (except, perhaps, extending article 50), and the two sides already agree on the fundamentals.

It must be stressed that this status quo transitional arrangement, desirable as it may be, does not resolve the fundamental issues of Brexit. One day, the UK will have to choose what it wants: sovereignty or market access. Also, it doesn’t prevent there from being a cliff-edge at the end of the transition, especially if it’s only a couple of years long. (An indefinite transition is desirable but politically implausible; an easily extendable deal would do the trick). However, it buys time – an invaluable resource when the clock is ticking.

• Piet Eeckhout is dean of the faculty of laws at UCL, Oli Patel is research associate at UCL’s European Institute