I am not sure whether Margaret Thatcher would have subscribed to today’s neoconservative dogma on Israel or not—an issue that commentators have been debating here, here, and here—although the heads of the Henry Jackson Society, the leading neocon outlet in Britain, are certain that she would.

But in any case, British policy on the Arab-Israeli conflict has traditionally been overseen by the so-called “Arabists” in the Foreign Office—perceived to be the bastion of an elite detached from Jewish concerns—who operate on the axiom that what is good for Saudi Arabia and the other Middle Eastern oil states is good for Great Britain and vice versa. Occasionally pressure from the pro-Israeli Americans modifies that position.

Thatcher, like former Labour Prime Minister Harold Wilson, may have been considered a Friend of Israel (FOI), but unlike American presidents who were FOI, her ability to shape British policy towards the Jewish State was quite limited. (This episode of “Yes, Prime Minister” illustrates that point.)

More importantly, British foreign policy under Thatcher and her predecessors had been based, since the late 1940s, on the expectation that the United States should and would replace Great Britain as the hegemonic Western power in the eastern Mediterranean (overseeing Greece and Turkey) and later, after the Suez crisis, in the Middle East and Persian Gulf, following Britain’s imperial retrenchment. Postwar Britain lacked the economic and military resources to continue securing access to oil in the region, and for dealing with the never-ending conflict between Israelis and Arabs.

Hence when Thatcher warned the first George Bush that “this is no time to go wobbly” and that he had to force Saddam Hussein out of Kuwait, she expressed the traditional post-Suez British view of the need to present a common Anglo-American face in the Middle East. My guess is that she would have pursued the same kind of policy that Tony Blair, her Labour successor, embraced during the second Bush’s Iraq War—perhaps with less enthusiasm about promoting democracy and nation-building.

The problem is that the United States is beginning to exhibit the same need for imperial entrenchment in the Middle East that Britain experienced after World War II, when it started reducing its military footprint in the region and got fed up with trying to resolve the conflict between Jews and Arabs.

The Brits ended up passing the Middle East torch to the Americans. But now, despite mounting federal debt and military fiascoes in Iraq and Libya, Americans seem to be stuck in the region as a declining hegemonic power, while the British (and French) continue free-riding on U.S. power. The “special relationship” has proved to be one-sided.

It’s true that the British have been more inclined to deploy troops to Iraq and Afghanistan than other U.S. allies have been, and the British joined the French in playing an active role in Libya. But in reality much of the military, and by extension financial, burden of “doing the Middle East” still falls on the United States, with Britain and other NATO members resisting pressure to increase their military budgets. In fact, both London and Paris have been pressing Washington to get more directly involved in the Syrian civil war and to take a more assertive position vis-à-vis Iran’s nuclear aspirations, knowing full well that the U.S. will wind up paying most of the costs for new military interventions in the Middle East.

So I am not sure where Thatcher, who came to power during the height of American economic and military dominance, would stand on these issues. Would she be urging Barack Obama not to go wobbly on Syria and Iran? Or would she be calling for a major increase in British defense expenditures and for the strengthening Anglo-French military ties (as well as cooperation with Poland and Turkey), as part of or separate from NATO? Thatcher would probably continue to accentuate her Euro-skepticism. But what would her response be to the rise of German economic and political power, and would she try to form counter-balancing alliances? That no one can answer these questions with any confidence goes to show how much the world political and economic environment has changed since Thatcher’s time.

Thatcher had always operated under the assumption that America the Superpower would be there to protect Britain and its allies against global security threats like Nazi Germany or the Soviet Union. But without such a threat on the horizon, and under an international system that is taking a more multi-polar shape as American power erodes and the U.S. “pivots” to East Asia, it is doubtful that the relationship between the United States and Britain (which will cease to be “Great” if Scotland chooses independence) will remain central to either country’s foreign policy, or that the notion of a united Anglo-American front in the Middle East continues to be relevant.

American and British neocons may have been mistaken about the so-called Islamofascist threat highlighting common interests between Washington and London, particularly in the Middle East. But their complaints about President Obama’s decision to return the Churchill bust that the Brits had loaned to his predecessor may have had some validity—in the sense that America’s first “Pacific president” perhaps doesn’t feel that the relationship with the British is so special after all.

Such an attitude may reflect more than just Obama’s personal unsentimental view of our “cousins” across the Atlantic. Instead, it could turn out to be the start of a long-term trend that emerges from changing global priorities (away from the Atlantic and Middle East to the Pacific) and national demographics (less Anglo, more Latino), all of which make it less likely that what a British prime minister does in the future will matter as much to America’s policymakers as in the days of Bush I and Thatcher or Bush II and Blair.

Leon Hadar, senior analyst at Wikistrat, a geostrategic consulting group, is the author of Sandstorm: Policy Failure in the Middle East.