I can’t say whether Montgomery considered running for any political office, but my political knowledge can shine some light on the situation.

I don’t know much about the French system but I know that the American system provides an easy enough route for election to the presidency for anyone who has the resources (I.e. trump)

Now for the British system. Britain operates under a parliamentary system which means the executive (cabinet/government) is made up of the party who holds a majority in parliament (as opposed to the American system which directly elects the executive through presidential elections). So to become the prime minister an individual would have to be the leader of the party who manages to gain the most seats in Parliament after a general election. Furthermore, to be the prime minister you’d have to be a member of Parliament. So if they were to stand a chance in higher office they’d first have to rise high enough in a party’s ranks to become a candidate for a constituency’s seat in Parliament and then win the seat, and then become the leader of their party.

Another point to note is the leadership of the parties at the time. First of all there was a general election two months after Germany’s surrender (Germany surrendering in may and the election being in July). So a general would have to wait another five years until the next election in 1950, (although this was only two years before Eisenhower ran for president) to merely run for Parliament. And even then it’s fair to say that they wouldn’t stand much chance of competing against the leaders of the two main parties anyway (Clement Attlee of labour had managed to win the Labour Party one of its first majority governments ever against the, I would assume, popular Winston Churchill who led Britain throughout the war, and yet Churchill was still leading the conservatives meaning a general trying to get into politics would be competing against extremely popular heavyweights of the two parties up until at least a decade after the end of the war).

So in my opinion , I can’t comment on whether any generals did consider running for office, however I can point out the practical difficulties they would have faced as a result of the British electoral system.

Notes: I am kind of drunk while writing this so please excuse any mistakes such as leaving out the 1951 election.

Although I would consider it unlikely that many British generals considered entering political life after service in the Second World War, especially Monty (who remained in the army until the age of 70), it is also worth noting that the structure of British parliamentary democracy is far removed from that of the French or American governmental systems, and consequently would make it unlikely that they would ever achieve high office.

This is due to the fact that the (modern) British government, i.e. the executive branch, is drawn directly from the legislature, with the largest party forming the government, the leader becoming the Prime Minister, and their close advisors becoming the cabinet - the heads of ministerial departments, such as Health or Education. This system therefore militates against occurrences like that in the US, whereby a political outsider can win a party nomination and enter the presidential race in a comparatively short time frame; this simply is not possible in Britain. Many Prime Ministers will have spent much of their career as a Member of Parliament, and before that, in other positions within a political party, gaining experience and influence within the party before taking a leadership position that could enable them to become head of government. Military officers leaving their careers would therefore have to seek nomination by a party, win a constituency election, become the leader of their party, and then form a government (by winning a general election), and it is unlikely that they would be able to achieve all of these, above all leadership of a party, in a short time frame after leaving the army, particularly as many British generals served until retirement. Alanbrooke for example, served until the age of 62, and then became commandant of the Honourable Artillery Company until 70.

It is however worth noting that, although none of Britain's more prolific generals from the Second World War ever achieved high office, Britain has had professional military officers attain high office prior. Winston Churchill in fact had previously held a commission in the British Army, both prior to and during World War One, and served in both the cabinet and in two different governments as Prime Minister. However, the most noted example of a British general becoming PM is most likely the Duke of Wellington, who oversaw two short governments between 1828 and 1834, although this was prior to the development of the modern British party system.

There is no evidence of political ambitions, in fact just the opposite. After the passing of the Parliament act in 1911 effectively meant all PMs had to come from the commons. When Monty accepted the title of Viscount of Alamein and joined the House of Lords, he ruled himself out of becoming Prime minister. At the time, there was no way of giving up a title.