LONDON — To hear some British politicians tell it, they are mere servants. They can only execute popular will, whatever the cost to the country or themselves. To do otherwise would be to betray democracy itself.

“The will of the British people is an instruction that must be delivered,” Prime Minister David Cameron said after voters narrowly approved leaving the European Union in a 2016 referendum, though this meant both his resignation and, in his telling, devastation to the British economy.

Yet lawmakers also believe they must determine for themselves how to serve Britain’s best interests. Prime Minister Theresa May, Mr. Cameron’s successor, justified her plan for withdrawal, or Brexit, as the best way forward, even if it was not the most popular.

Voters seem to share these dual expectations. The British government, many believe, should first and foremost safeguard the national good, including from the whims of public opinion, which has flipped several times since the initial vote. But it must also respect public opinion, as captured in that nearly three-year-old vote, above all else.