Do Cabinet Ministers have powers over the Prime Minister?
There are factors which strengthen Cabinet Ministers positions against the Prime Minister:-
Ministers run large Departments on a day-to-day basis, dealing with many issues and have a large civil service with technical expertise and their own political advisers. They also have overall responsibility for a range of Agencies and Quangos. The Prime Minister can intervene, though in practical terms not on everything, and, although he or she also has a civil service and political advisers, intervening within a Department takes a lot of effort. The Prime Minister has to spend time coordinating issues that cut across Departments and may not have time to look at many purely Departmental issues.
Ministers are politicians who are often major figures in their Party and so may have a power base in both the the Party in the country and the Parliamentary Party. They may be hostile to the Prime Minister or rivals for the office. Tony Blair had to appoint Ministers who were supporters of Gordon Brown and this gave Brown power to delay or stop many policies.
Ministers have links to the media and, through their Departments, to interest groups. They can leak information and brief journalists against policies that the Prime Minister wants to pursue. The Department can warn interest groups of a policy detrimental to them that the Prime Minister wants to pursue so that these interest groups can put out adverse publicity against it.
A combined revolt by the Cabinet can prevent a policy advocated by the Prime Minister and they can even bring the Prime Minister down as happened to Thatcher in 1990. Ministers can be sacked but can be a focus for dissent on the backbenches. The resignations of her Chancellor of the Exchequer, Nigel Lawson, and Deputy Prime Minister, Geoffrey Howe, and their resignation speeches in the Commons severely weakened Thatcher.