LONDON — Over the past 40 years, the Brits have become used to watching their prime ministers swing their weight around on the European stage.

Margaret Thatcher’s so-called hand-bagging to secure a budget rebate gained semi-mythical status, as did Gordon Brown’s controversial decision to dodge the signing of the Lisbon Treaty.

So far, Prime Minister Boris Johnson’s ventures “on the Continent” echo, at least superficially, the decades during which the U.K. was at the heart of EU decision-making.

That won’t last.

What British politicians — Johnson especially — keep misunderstanding about Brexit is that leaving the engine room of EU policymaking does not mean being able to sail off happily on your own.

Simply put, few in the U.K. have come to terms with what becoming a neighboring state of the EU will mean in practice.

The U.K. can leave EU institutions, but it has not yet found a way to physically move the British Isles to a different part of the world. The morning after Brexit day, Britain will still find itself located next to a huge trading bloc with increasingly state-like structures.

U.K. politicians are scrambling to lay blame on the EU for the ever-increasing likelihood of a no-deal Brexit, but they have failed to grasp a key aspect of life outside the EU: London will soon be more reliant on the bloc’s goodwill than ever before — especially in the event of a no-deal Brexit.

If the U.K. leaves the EU without a deal on October 31 — which Johnson has insisted he is prepared to do, despite the House of Commons voting to stop him — U.K. politicians will have to pause their EU-bashing, and humbly beg Brussels to put in place a raft of measures averting the worst economic effects of a messy exit. These would be mitigating measures the EU can terminate at any time.

Simply put, few in the U.K. have come to terms with what becoming a neighboring state of the EU will mean in practice.

The promise of Brexit — peddled by Johnson and his chief of staff, Dominic Cummings, during the 2016 campaign — was to give British voters sole control over the U.K.’s future. In truth, it means giving up a significant source of control: The ability to block European policies that might contradict British interests.

Just ask the EU’s other neighbors.

Brussels, it turns out, has a long reach. EU laws have a ripple effect on countries that neighbor the bloc, as they force non-EU governments to adjust the way they organize their borders, laws and trading practices to ensure they can maintain access to the Brussels-led single market.

After Brexit, the U.K. — much like Turkey, Serbia, Algeria or Ukraine — will find itself in a position of having to adapt to whatever legal changes happen at an EU level, with no control over how these decisions are made.

And if the experience of current neighboring states is any indication, maintaining a relationship with the EU that also serves your national interests is no easy feat.

For countries like Norway and Switzerland, the ability to sustain a close and stable relationship with Brussels depends entirely on politicians and voters believing it’s in their best interest to do so. Current tensions between Switzerland, where Euroskepticism is on the rise, and Brussels are a good example of how quickly a breakdown of political consensus can destabilize that relationship.

For some countries, including Tunisia, Albania and North Macedonia, access to the EU is so crucial for business they are willing to accept oversight from Brussels. In the case of Turkey, the level of interdependence with the EU is so high that Ankara has agreed to keep a shared customs union and effectively freeze Turkey’s accession process, despite deep tensions over hot-button issues such as Kurdish diaspora politics and border management.

British Brexiteers and quite a few Remainers still seem mesmerized by visions of a powerful Britain with an undamaged political and diplomatic status in Europe.

Russia, too, has been forced to sustain its engagement with EU institutions, as a result of its energy and export sectors’ dependence on European markets.

Britain will not be able to escape a similar fate.

Nor will a no-deal scenario be a get-out-of-jail-free card. On November 1, the U.K. would no longer be bound to the EU by any formal agreement but it would immediately become dependent on Brussels for cooperation in mitigating the worst of the disruption to trade, the economy and its borders.

Given that the EU could turn its back on the U.K. at any time, British politicians, officials and businesses will face many of the same diplomatic and political dilemmas as their counterparts in countries like Turkey, Serbia or Iceland.

British Brexiteers and quite a few Remainers still seem mesmerized by visions of a powerful Britain with an undamaged political and diplomatic status in Europe. These dreams are increasingly divorced from the U.K.’s real geopolitical position.

The U.K. is not exchanging its EU membership for more control. It is giving it up for a spot in the EU’s sphere of influence.

Alexander Clarkson is a lecturer in European studies at King’s College London.