Why is it that the power of the Prime Minister is so subject to change and variation?

Firstly the power of the Prime Minister is largely dependent on the majority the party they lead, has in the House of Commons. Should a Prime Minister command a party with a large majority in the House of Commons then this allow the Prime Minister to pass their government's legislation through parliament with little concern for the interests of either opposition MPs or the more rebellious MPs within their own party. However should the Prime Minister find themselves with only a small majority in the House of Commons they may find themselves being 'held to ransom' by their own MPs who will force the PM to change parts of their legislative program otherwise they will vote against it, and see the government defeated and unable to pass legislation. Secondly the PM's power is dependent on their own personal style of governance. Many PMs have often granted their ministers a large amount of autonomy in regards to policy, such as Winston Churchill, thus diminishing the power of the PM themselves. However some, such as Tony Blair and Margaret Thatcher, have often exercised a large degree of control over their government ministers, reducing their autonomy and increasing the power of the PM. Thirdly the perceived popularity and success of a PM will impact their power. A PM who is thought to be popular and successful will often exercise greater power as their party will not be able to justify removing them from the leadership. Thus the PM is able to act more freely within their own party without risk of retribution in the form of a leadership challenge from within. However a PM who is deemed to be more unpopular and unsuccessful, is far more likely to face challenges to their leadership as the party becomes concerned over their electoral prospects and success in government. In this situation the PM may be forced to please aspects of their party in order to maintain their position and prevent a 'coup'.