David Cameron, U.K. prime minister and leader of the Conservative Party, delivers his victory speech outside 10 Downing Street following the 2015 general election, in London, U.K., on Friday, May 8, 2015. (Jason Alden/Bloomberg)

THE SURPRISE victory of the Conservative Party in Thursday’s election spared Britain from the widely predicted scenario of a hung Parliament and the political turmoil that would have produced. It means the government will not have to depend for support — as a victorious Labor Party would have — on the surging Scottish National Party, which aims to disarm and dismantle the United Kingdom. After five years of coalition rule, Prime Minister David Cameron will now lead a Tory-only cabinet and can continue an economic program that has enabled a more robust recovery from recession than almost anywhere else in Europe.

Mr. Cameron’s victory nevertheless amounts to something less than good news for American supporters of Britain and the “special relationship” between the two countries. Having overseen a broad retrenchment of the country’s military power and place in global affairs during the past half-decade, Mr. Cameron will be preoccupied during his coming term with preventing two developments that would be disastrous for the country’s international standing: the withdrawal of Scotland from the United Kingdom and Britain’s exodus from the European Union.

Another vote on independence seems a likely consequence of the Scottish National Party’s historic sweep of seats — even if its popular leader, Nicola Sturgeon, insisted that its agenda for this election did not include that demand. Ms. Sturgeon shrewdly appealed to the majority of Scots who voted against independence last year to support her party for its left-wing platform, including a promise to “end austerity”; the result was a massive shift of voters from the Labor Party.

In England, many voters appeared to have turned against Labor precisely because of the prospect that it would depend on the Scottish party to form a government. They also doubted the economic program of leader Ed Miliband, who, in promising tax increases and price controls, steered away from the center ground occupied by former Labor prime ministers Tony Blair and Gordon Brown. In that sense, the election revealed a geographic split along ideological as well as national grounds, with Scottish voters favoring a socialism the rest of the country rejects.

Mr. Cameron has promised to support a greater devolution of power to Scotland but may find it hard to brake the political momentum toward another independence vote. Meanwhile, he will have to manage a problem of his own making: a pledge to renegotiate the terms of Britain’s E.U. membership and hold an in-out referendum by the end of 2017. That will involve tough negotiations with European leaders, who will be reluctant to grant Mr. Cameron concessions on issues such as immigration, and with the Euro-skeptic wing of the Conservative Party. More than one British analyst pointed out Friday that Mr. Cameron’s one-party majority may end up working against him as Tory hard-liners do their best to sabotage the prime minister’s plan to keep Britain in the European Union.

This inward focus and more cuts in the British military are likely to perpetuate what has been a slow deterioration of a U.S.-British alliance that has been critical to U.S. global leadership in the post-Cold War era. President Obama, who has overseen his own international retrenchment, may not be much troubled, but a successor who seeks to restore American power in the Middle East and elsewhere may have to find a way to do it without Britain.