Of course, to become party leader, Johnson has to be am MP. His second term as Mayor ends in May 2016. At the moment there is nothing to stop him holding two posts- if I were Cameron I would note that under the Police Reform & Social Responsibility Act 2011 anyone who is a Police & Crime Commissioner is barred from being an MP, note that the Mayor of London is effectively the Police & Crime Commissioner for Greater London, and so have a quick one-line Bill amending the House of Commons Disqualification Act 1975 to add Mayor of London to the positions that leads to disqualification from the House of Commons.
Purely to clear up a little anomaly of course.
This leads to one question- if Cameron were removed as party leader, could he remain Prime Minister?
Until July 1965, the Conservatives didn't elect a leader- one simply emerged as a result of questions like "Wab or Hawold?" being asked. Indeed, until October 1922 there wasn't a formal leader when the party was in Opposition- there would be separate leaders in the House of Commons and the House of Lords.
One important thing to note is that we have a coalition, and so we need to look at our last experience of a coalition- one that lasted, in various permutations, from August 1931 to May 1945.
In August 1931, realising he would have to introduce an austerity programme (sound familiar?), and would not have support from his Labour colleagues, Ramsay MacDonald formed a new Government with support from Conservatives and Liberals. When the Government was formed, the party leaders were:
There was a general election in October 1931, and the Liberals had split. After the election, the leaders were:
So, the party leaders were holding quite senior positions- Lord President of the Council is the post held by the current Liberal Democrat leader, Nick Clegg.
The next change was the withdrawal of the Liberals in September 1932, leading to the final split between the Liberals and National Liberals. This neccesitated a Cabinet rehsuffle, with the party leaders being:
There is a little reshuffle in December 1933, when Anthony Eden replaced Baldwin as Lord Privy Seal (which ceases to be a Cabinet position- similar to today's situation).
Then there is MacDonald's resignation as Prime Minister in June 1935- just 5 months before a general election in which he would be defeated in Seaham by Labour's Emmanuel Shinwell- and the party leaders are then:
Note that MacDonald became Lord President of the Council, which he kept even after losing his seat (he was returned in the Combined Scottish Universities by-election in January 1936 caused by the death of the Scottish Unionist Noel Skelton, who had died just 8 days after the general election. In this by-election the runner-up was Andrew Gibb, of the Scottish National Party, which had emerged on the scene in the 1935 election). MacDonald resigned fron the Government in May 1937 and died 6 months later.
In May 1937, Baldwin was replaced by Neville Chamberlain as Prime Minister, and the party leaders were:
Chamberlain replaced Baldwin as party leader 3 days after becoming Prime Minister- a reversal of current normal practice.
May 1940 saw the radical change of Government, with Winston Churchill becoming Prime Minister, and Simon becoming Lord Chancellor. The party leaders were:
In October 1940, Chamberlain resigned both as Conservative leader (being replaced by Churchill) and Lord President, dying the following month. Attlee and Brown both remained in the Government until the end of the coalition in May 1945.
What does this tell us? There is no requirement that the leader of a coalition party has to be in the Government. And, as the Chamberlain/Churchill example shows, there is nothing wrong with having the situation where the Prime Minister is from a party, but its leader is holding another position.
Consider this scenario. It is October 2014, and it is time for Cameron to announce his choice of European Commissioner to take office the following month. No-one is surprised when Clegg is chosen, and he resigns as party leader, from the Cabinet and is given an Office of Profit under the Crown which leads to the good people of Sheffield Hallam going out to vote in one of the last (and maybe the actual last) by-election of this Parliament.
As has happened when previous Liberal Democrat leaders have resigned/been knifed in the back, the deputy leader takes over until a by-election is held. In this case, this would be Simon Hughes, the MP for Bermondsey & Old Southwark.
So, should Hughes then enter the Cabinet? What if he doesn't want to?
In this case, someone had to take Clegg's position as number 2 in the Cabinet. The choice would be between Vince Cable, the Business & Innovation Secretary; Ed Davey, the Energy & Climate Change Secretary; and Michael Moore, the Scottish Secretary. Although, depending on the outcome of the Scottish referendum, Moore would either be on a roll (and hence ideal to take the number 2 place on a short-term basis?) or else seen as a poltiical loser, the man who lost Scotland on his watch.
Would Hague have to be moved slightly? Cable, Davey and Moore are all Secretaries of State, and you cannot have one of them senior to the First Secretary of State. Either whoever Cameron chooses to take over as number 2 for a short-term basis is moved to replace Clegg at the Cabinet Office (but wouldn't that imply he wished them to become leader?) or they become First Secretary of State and Hague is given a title like Lord Privy Seal or Chancellor of the Duchy of Lancaster, and a Conservative is moved to the Cabinet Office and becomes Lord President of the Council.
And if Cameron appoints someone as number 2 on a short-term basis, he would appear to be giving an opinion on another party's leadership election. The sensible thing would be for one of the 3- Cable, Davey and Moore- to rule himself out as a leadership contender, and then he can be promoted by Cameron without it coming across as interfering by Cameron in an internal Liberal Democrat matter.
And if Hughes would enter the Cabinet, then he would have to be First Secretary of State if he were given a department (other than the Cabinet Office or Treasury) to run, for reasons given above.
Now consider a second scenario- it is May 2015, and the election result is similar to the one 5 years earlier. The Government continues, but the Conservatives want to remove Cameron.
That takes time, though. 15% of Conservative MPs have to write to the Chairman of the 1922 Committee to ask for a no-confidence motion. And then if a majority of Conservative MPs vote to remove Cameron, he is out and a new leadership election is held- and if the MPs choose more than one candidate then a leadership election takes about 3 months.
So, if Cameron refused to resign as party leader, we are looking at August 2015 before his replacement is chosen.
And there is a little trump card he has.
Curiously for a monarchist party, the Conservatives have removed one of the Queen's personal prerogatives- under the Fixed Term Parliaments Act 2011 she no longer dissolves Parliament on the Prime Minister's request.
In theory, if Cameron were ousted as Conservative leader, and a 3 month long leadership election is triggered, then he could present the following motion to the House of Commons- This House has no confidence in Her Majesty's Government.
If it does have confidence, then he can tell his party that Parliament has confidence in the Government he leads. If it doesn't, then the House of Commons has 14 days to pass a confidence motion in someone else (or in him)- and if it doesn't he can ask the Queen to dissolve Parliament.
There is a solution, and it involves removing the Queen's other personal prerogative- choosing a Prime Minister.
Under the Scotland Act 1998 the Queen appoints the Scottish First Minister- but she appoints the person whom the Presiding Officer tells her has been chosen by the Scottish Parliament.
Could this be done at a Westminster level? Normally, the House of Commons meets for the first time the Wednesday after the general election. Then there a couple of days of swearing in.
So, with appropriate legislation passed, the Speaker of the House of Commons would, after the swearing in of MPs, announce that he or she would be meeting the Queen the following week and will be advising her of who to appoint as Prime Minister or whether the current Prime Minister should stay in office- and he or she can only advise her to appoint whoever the House of Commons chooses, in a series of exhaustative ballots, with the lowest placed candidate dropping out each round.
If there is a hung Parliament, then this gives the parties a couple of weeks to sort out a coalition- but also provides a deadline, namely the day of the meeting between the Queen and the Speaker.
And if someone is elected by the House of Commons, then it can be deemed to have confidence in a Government led by them, regardless of whether this is just after a general election or mid-term as a result of a Prime Minister dying or resigning, or losing a no-confidence motion.
In Germany, the Bundestag elects the Chancellor, but the person it elects need not be a perty leader (e.g. Gerhard Schroder in September 1998).
Why not follow this system?
Now, there is one practical matter. Consider the scenario where Cameron is elected Prime Minister by the House of Commons, but is removed from the party leadership and replaced.
At the moment, Clegg decides on which Liberal Democrats hold the posts in Government allocated to his party. But surely, if Cameron were to be Prime Minister without being party leader, shouldn't the Conservative leader be deciding who the Conservative minister should be? In that case, the Prime Minister's only say in the Government composition is which posts go to which party.
One solution would be for the Prime Minister to draw up the Government, and only be advised by the leaders of the parties in the Government.
In short, there is nothing to say that the Prime Minister has to be a party leader, and the situation where he or she wasn't would put us in interesting constitutional waters (decide for yourself if that's a euphemism for "all at sea")