How does the UK not have a Vice Prime Minister? 😲
Because the U.K. has a parliamentary system of government, not a presidential one. The Prime Minister is not elected, a parliament is. And it decides who is, and remains, as prime minister. Member of Parliament being representatives, elected to use their best judgment on behalf of their constituents no matter whom they voted for, and not simply delegates. And part of that best judgment is in deciding which amongst them should form the government.
Of course in practice people vote for parties, in the knowledge that a chosen candidate will support their party leader as Prime minister.
Constitutionally the Prime Minister is appointed by the Queen, in reality she appoints the person who commands the support of Parliament. Almost always this is the leader of the party which has a majority, although in rare occasions, such as after the 2010 general election, no party has a majority and so the different parties meet to form a coalition or arrangement where a majority will support a particular party's leader.
Importantly, at any point Parliament can vote that it has no confidence in a prime minister. Or the governing party can vote it has no confidence in its leader. In both situations it leads to a prime minister resigning. Depending on the circumstances this will usually lead to the governing party electing a new leader or, very unlikely as it would need cross-party support, Parliament supporting someone else, who will be appointed Prime Minister by the Queen. Or it could lead to a new general election being called.
This not only applies within Parliament but also within the cabinet, as this is who technically governs. The Prime Minister effectively has overall control because they get to decide the cabinet. But if a majority of the cabinet did not agree with the Prime Minister, they would normally reflect their party as a whole and have the ability make things difficult for the Prime Minister to the extent of forcing a vote of confidence within the Party to oust them. This is the story of Theresa May's government, which lead to Boris Johnson becoming Prime Minister through a leadership contest after May was forced to resign.
The cabinet, incidentally, are also constitutionally appointed by the Queen, but this is done on the advice of the Prime Minister.
So constitutionally you cannot have a Vice Prime Minister because even the Prime Minister only stays in office due to the continued support of Parliament that can be taken away at any moment. You cannot have a second-in-command with more job security that the leader!
But some governments have named deputy prime ministers, a cabinet member who will take place of the Prime Minister when they are unavailable. Whether that is to answer questions when they are out of the country or to take charge when they incapacitated.
But it is not itself a constitutional role, unlike cabinet secretaries, and so does not come with a salary over what they are paid as a member of parliament or minister. So the position is not often used, and when it is it is normally for political reasons. Tony Blair moved the Labour party more to the centre, so in his government he had John Prescott as his deputy to keep the traditional left on board. When David Cameron failed to gain an outright majority for the Conservative party, he formed a coalition with the Liberal Democrats and so made their leader, Nick Clegg, the Deputy Prime Minister, to show it was not a Tory government but in name.
Johnson had decided not to name anyone as Deputy Prime Minister in his government, however he appointed Foreign Secretary (the Secretary of State in U.S. politics) to lead the government before he went into hospital. And because constitutionally it is Cabinet, appointed by the Queen, and not the Prime Minister that actually governs this is just the normal working of government.
Had Johnson been incapacitated before being able to name someone to take his place, the cabinet would likely have decidedan interim leader amongst themselves. Which due to the country being in a state of crisis, their party would have supported. Though technically it would have been up to the party to appoint a new leader in accordance with its own internal rules.
