Our friends in the rebellious Colonies have the still active remedy of impeachment for those in office who, one might say, go off the rails, and other remedies as well. In the UK, impeachment is now considered ‘obsolete’ as a means of removing Crown officials, but ‘obsolete’ does not mean ‘defunct’:
As a House of Commons Paper puts it (in the link at the bottom to the pdf.):
It was a medieval means of removing the protection given to a royal servant whom the Commons found objectionable but could not otherwise persuade the Crown to dismiss.
Of course, different parts of the Commons may find the current First Lord of the Treasury ‘objectionable’ for widely varying reasons, either that she is not an avowed openly Marxist destroyer, or that she is simply a ‘Tory’, or that she is far from satisfactory in terms of her integrity.
But we appear for now to be in a situation where neither a vote of no confidence in the House of Commons on Mrs May’s government, nor a vote in her Party via the 1922 Committee in her as a leader, appear to be imminent or practicable.
As the Commons briefing paper notes:
No Prime Minister has ever been impeached. Ministers have been impeached, but those instances occurred before the modern concept of the Cabinet was established.
The first edition of Erskine May, published in 1844, describes impeachment as: “the commons, as a great representative inquest of the nation, first find the crime and then, as prosecutors, support their charge before the lords; while the lords exercising at once the functions of a high court of justice and of a jury, try and also adjudicate upon the charge preferred”.
Let us look at some of the criticisms of impeachment:
Impeachment operated in an era when Parliament and the courts had very limited oversight of government power. Different mechanisms have developed in modern politics to allow for the scrutiny of the executive. These include parliamentary questions, inquiries by select committees and independent committees of inquiry. The growth of the doctrine of collective cabinet responsibility, and the use of confidence motions have both contributed to the disuse of impeachments in modern times. Judicial review also now provides an effective check on the legality of the actions of public officials and government ministers. The impeachment process, last attempted in 1806, has not been revised to reflect the fundamental changes that have occurred in Parliament.
What use is a Parliamentary Question when the Prime Minister has misled the House and the Country for over 2 years? Who would trust an answer now?
Select Committees? All very well for getting some MPs to look at something in-depth, but when there is a cowpat in the Ballroom of State, the answer is steaming away in front of you for you and all your guests to see.
Collective Cabinet responsibility? The Cabinet largely remains in place, happy for this farce to carry on. They are not acting responsibly.
Confidence motions? As noted, there is a confidence motion procedure for the government, which due to the Fixed-Term Parliaments Act now has a cooling-off period, and it is not the government that is the major problem (although it is a big problem generally), but the leader of it.
Party confidence motions are internal matters, nothing to do with Parliament.
Judicial review: Sir Edward Coke left the Bench long ago. Judicial Review is not applicable to this sort of situation.
The beauty of impeaching the Prime Minister would be:
1. It would enjoy cross-party support, helping to ‘heal the wounds’ caused by the contentious issues we face 
.
2. It would leave the current Parliamentary composition intact. After all, it is removing a Crown Servant, not a Member of the House. Mrs May would remain an MP.
3. It would leave Mrs May as the unelected Leader of the Conservative and Unionist Party, and put her in the same situation as another notorious appeaser, Neville Chamberlain as leader of the Party and an MP but not Prime Minister. Not quite following the Joseph Chamberlain that she aspires to emulate, but as close as we can manage for now.
4. It would revive the prestige of Parliament, at a time when Mrs Battenberg’s presumed function of ‘to advise, encourage and to warn’ appears to be obsolete. After all, it has recently (in Constitutional timeframes) been used in the United States, an offspring jurisdiction of England, so why should it be ‘obsolete’? We may have reached the lacuna where the remedy has some use.
5. It would (or should) save us paying Mrs May a Prime Ministerial pension later on in a richly-deserved retirement. That will help to reduce our ballooning public sector pensions liabilities.
6 It would cement Mrs May’s place in history, whether or not the Lords were to convict.