The recent unveiling of a bust of Sir Winston Churchill in the Capitol Building offered a reminder of the long-standing special relationship between Great Britain and the United States. But there is something that keeps the relationship special today which the British shy away from: Britain’s membership in the European Union.

Since the 1960s, successive American administrations—Democratic and Republican—have supported the UK’s participation in European integration, a project the United States encouraged in order to help unite Western Europe after the Second World War.

Today, both the EU and Britain’s participation in it are acquiring new importance. The emergence of a multipolar world and the decline of U.S. unilateralist impulses, mean Washington increasingly needs to work with like-minded allies. Gone are the days when Washington feared that a more cohesive EU would lead to a transatlantic divorce. To the contrary, a stronger EU with the UK at its core is now seen as the best way of ensuring that Europe remains a relevant American ally.

For all the talk of an ‘Asian pivot,’ the United States remains a European power and Europe remains vital to U.S. interests. The United States and Europe are the foundation of the world’s most powerful military alliance, and are linked by the most vibrant and deep economic relationship in the world. Shared values and ideals underpin the partnership and have enabled it to outlast the Cold War.

It is the potential—and ambition—to fully exploit the transatlantic relationship that lies behind the U.S.-EU negotiations for the Transatlantic Trade and Investment Partnership (TTIP), a proposal that has strong British backing. If successful, TTIP would play a major role in modernizing a transatlantic partnership forged in the early days of the Cold War and in ensuring that Atlantic norms guide the emergence of a post-Western world.

Yet at precisely the moment Washington is looking to invest in U.S.-EU ties to renovate the transatlantic relationship, the UK is threatening to leave the union. British politicians overestimate the global influence they would have outside the EU and underestimate the harmful implications of their withdrawal on the long-standing ‘special relationship.’ It is especially ironic that the Conservative Party, which for decades has attached so much importance to the ‘special relationship,’ threatens to undermine the UK’s ties to Washington with a reflexive Euroskepticism.

What British advocates of a withdrawal fail to understand is that the United States would first and foremost assess the implications of a UK withdrawal by what it means for America’s relations with the rest of the EU. Relations with Britain would be an important, but ultimately secondary question, reflecting Britain’s reduced geopolitical standing from withdrawing from a relationship central to its international standing. Other powers such as Russia or China would follow the same path.

An EU without Britain would be a more difficult place for the United States to do business. Both the United States and the EU would suffer from the loss of one of the most Atlanticist, globally ambitious, and liberal economies in the Union. The departure of the UK would deprive the EU of a leading pro-reform voice at a moment when the United States is particularly keen on seeing the Union take important changes. It would also likely reinforce the inward-looking tendencies of the EU, which exasperate Washington. Finally, a UK departure from the EU—and therefore from the TTIP—would likely require the United States to negotiate and arrange for a separate trade agreement with the UK.

While the UK won’t vanish from European politics, its influence would diminish if it left the EU, meaning Washington will have to bypass London and deal with other EU partners. Despite recent tensions over NSA spying activities, there will be no shortage of applicants to be America’s new closest friend in Europe. Indeed, British backers of the special relationship with Washington should not overlook the fact that the United States has long-standing close relations with other EU members, including France. Germany, meanwhile, will exert much more influence in Washington by leveraging its position as a leader within Europe than London will by serving as America’s ally outside the EU.

Of course U.S.-UK relations would remain close in the event of a UK departure from the EU, with continued cooperation on nuclear weapons, intelligence and special operations forces. But the UK should be careful in overestimating its global influence as an independent power in the twenty-first century. Significant, sustained cuts to the UK defence budget have harmed London’s fighting capability and its credibility in Washington. The UK Parliament’s rejection of an authorization to use military force in Syria also caused doubts in the United States about London’s enduring will to use military force. The United States would be far more interested in seeing the UK strengthen transatlantic ties through close strategic and defense cooperation with France and Germany than by attempting to serve as a robust but independent ally outside of European structures.

For Washington, the future of the UK and the EU are inextricably linked together and are critical to the centrality and relevance of the transatlantic link. Whether Britain remains in the EU is, of course, a decision only the British people must make. But they should not be surprised if a vote to leave leads the United States to reassess just how special the UK-U.S. relationship can still be.

Jeff Lightfoot is deputy director of the Brent Scowcroft Center on International Security at the Atlantic Council. He writes here in a personal capacity.

Tim Oliver is a Fritz Thyssen TAPIR Fellow at the Center for Transatlantic Studies, Johns Hopkins School of Advanced International Studies.

Image: Modified from Flickr/Rock Cohen. CC BY 2.0.