Though Labor leader Jeremy Corbyn is one of the few major figures in British politics publically calling for Theresa May to stand down from her premiership, the sentiment is rampant in Conservative constituencies and Establishment enclaves across Great Britain. The Prime Minister’s electoral gamble of trying to backfoot Mr. Corbyn’s troubled tenure, and increase her parliamentary majority, failed spectacularly.

To remain in power as leader of a minority party, Mrs. May must seek an agreement of “confidence and supply” — supply meaning spending — with Northern Ireland’s Democratic Unionists. The former Chancellor of the Exchequer, George Osborne, who was cashiered in July and edits the Evening Standard, calls Mrs. May a “dead woman walking.”

For all intents and purposes, the Prime Minister leads a caretaker government, awaiting a new head and new direction. Already rumors swirl that the Foreign Secretary, Boris Johnson, once her opponent for leadership, has been approached by five ministerial colleagues to stand against Mrs. May. While there may be little love in the country for the beleaguered Tory chief who shared scant authority with her colleagues, there is less appetite among Conservatives for the wounds that would be inflicted by a contest for the top job.

Particularly not with Brexit negotiations scheduled to begin in less than a fortnight (European Union officials will be merciless in exploiting Britain’s divisions to win concessions that undermine the determination of last June’s referendum). Mr. Corbyn’s rejuvenated Labor MPs will be salivating for any opportunity to assume government.

But there is an alternative to the choice of glumly following the maladroit Mrs. May or risking all on the vagaries of a leadership race. Simply turn the Prime Minister from a political liability into a benign figurehead for cabinet rule.

Titulary premiers were a commonplace of 18th-century British politics. Before rigid party identity became the House of Commons norm, the flexible composition of its membership often coalesced around policy (war and peace) or spoils of office (emoluments generously offered by the Crown for continued support of ministerial appointments).

Piqued at the conduct of peace negotiations by George III and Lord Shelburne at the end of the war with America, political adversaries Charles James Fox and Frederick, Lord North, schemed to overthrow Shelburne and, much to the King’s frustrated displeasure, formed government under the tutelage of the Duke of Portland. The Fox-North Coalition lasted only a few months, until in exasperation George consigned the Great Seals of State to more trusted hands, and employed patronage inducements to gain support for his inexperienced First Minister.

Thus began the heroic political career of Pitt the Younger, which lasted until Pitt died in office in 1806, in the midst of the Britain’s war against Napoleon and the parties at Westminster came together again to fight a common foe. Pitt’s first cousin, William Grenville, joined with Fox and other experienced statesmen in what history remembers as the “Ministry of All the Talents.”

Two centuries on and with such precedents in place, the task before the Tories is simple. Unite behind their leader on Britain’s issues of the moment: Brexit and the economy. Defense Secretary Fallon signalled this development in his plea for “collective government.” The Brexit players are already in place: Boris Johnson at the Foreign Office, David Davis as minister for exiting the European Union, and Liam Fox at International Trade.

A minor Cabinet shuffle at the week-end is a step in the right direction, with Michael Gove returning to government as Environment Secretary. Free-trade, limited-government sensibilities already animate the Brexit team, aided by the capable Chancellor of the Exchequer, Philip Hammond. More talent from the backbenches should be brought forward, too, such as the learned and persuasive Jacob Rees-Mogg.

Britain’s leader in cabinet government is mythologized as the “first among equals.” Never should this principle be more true than when a weakened Mrs. May must contend against strengthening winds of opposition at Westminster and Brussels. Toppling the Prime Minister at this moment of political uncertainty makes the nation a hostage to fortune. Keeping her at the head of a strong cabinet of Brexiteers and free market advocates loads the dice in Britain’s favor. At a time when the national honor is at stake, a return to stalwart Parliamentary tradition is a fitting Britannic tribute.

Mr. MacLean blogs for the Disraeli-Macdonald Institute at Canada.