There's 4 main reasons why, traditionally, British Army generals don't go into British politics as I see it. 2 have already been covered on the first page. The only person ever to have done it is the Duke of Wellington - and he didn't enter via the Commons, as would need to happen today.
1. The parliamentary system. In the US, a popular retired General need only get sufficient funding and subsequent backing of one of the main parties to run for President. In the UK, he'd need to join a political party first (well, the Conservatives), stand for election as an MP, wait for the leader of the party to quit or be ousted, hope to win the party leadership, and then hope to win the next election.
2. Commander in chief. Again, in the US the President is Commander in chief. The PM in the UK, actually, is not - the Monarch is, even if the PM exercises those powers. It's a minor point but an important one, as the British national psyche does not see the PM as someone who needs to have military knowledge or experience.
3. Island nation. Britain has always looked to her navy to defend her shores, rather than her small professional Army. It would be more believable for an Admiral rather than a General to form a government generally speaking.
4. The Armed Forces Bill. Ever since the Glorious Revolution and the subsequent Bill of Rights, it has been illegal for a standing army to be maintained in peacetime without consent of parliament - indeed the armed forces bill is first thing on the agenda for any new parliament. Thus in the UK the army is seen as existing at the behest of parliament - a General becoming the "head" of parliament doesn't really fit in well with this.
It should also be noted of course that there is really no official position of Prime Minister, which is a title given by convention, and one that didn't really come into popular use until the late 19th century. Indeed up until then, although de facto power has sat with the cabinet pretty much since the Bill of Rights, the myth was still perpetuated that the Monarch exercised the power on the advise of government, with the Monarch appointing and dismissing PMs and government as they saw fit.