The Prime minister's powers are descended from those held by the Monarch in previous centuries. As is the cabinet descended from the monarchs privy council. The twos related history gives us an understanding of why the PM has got power over the cabinet and they are not on level terms in decision making etc, The cabinet is always looking to the PM and following his lead. One reason for this is the fact that it is the PM who decides upon who is going to make up the cabinet, known as 'the power of patronage'.
Although this also applies to all areas of the executive it is an important point for cabinets. PM's tend to appoint like minded members of Parliament to be in the cabinet as this will lead to them having a more agreeable stance on the issues which the issues which the PM chooses to bring up in for example cabinet meetings, a working example of this is Tony Blair who would rather appoint Blairites than say Brownites for the reason that they will not go against him on important topics.
As well as the PM being able to appoint ministers he can also sack them, this leads to the ministers being more inline with his ideas even if in principle they disagree with them, for example Margaret Thatcher would sack 'wets' from her cabinet during cabinet reshuffles. Another of the PM's powers over the cabinet is his ability to organise Govt. business. Under this heading is included the ability to set the agenda during cabinet meetings, this can include keeping a topic of the agenda until it is at a stage where it is too late to go back on plans that have been deep set.
An example of this was the Millennium Dome, Tony Blair had kept it off the cabinet agenda but the cabinet had asked for the topic to be brought up. So Blair allowed this but then left the meeting, went to the Dome and was filmed by TV cameras announcing that it was to go ahead. As well as being able to set the cabinet agenda so that a certain topic is kept of the table is the fact that the PM can set up what are called Cabinet Committees. These are smaller cabinets made up of ministers from the cabinet but they are hand picked by the PM to deal with a specific topic.
This enables the PM to fill a CAB. COMM. with a team of ministers who are on his side and will bypass those in the cabinet which would have made a larger issue than necessary about the issue, Thatcher referred to them as 'wets'. It is said that it is in these comities that the real power lies and these claims come from the fact that Blair has made deals with at least 2 ministers about being one or Chairing certain comities, mainly Gordon Brown and John Presscot, whom both chair or at least feature in a number of CAB.
COMMS. Presscot was over heard on a train with Blair making a deal about which COMMS he would be on if he was to continue publicly supporting him. One other power which many PM's have used in recent years is in the fact that they have the ability to control minister's access to information through the circulation of cabinet papers. These are papers given to ministers before cabinet meetings so as they are able to join in on any discussion and be filled in on all details.
For example, Thatcher used to restrict which papers ministers got and sometimes didn't even send them out at all, one of her favourite tactics was to send the papers out at the 11th hour so that ministers were too tired to fully read and even if they did they would have been sitting up all night doing so. One famous occasion when this was used was in 1981 when Thatcher used this method to completely bypass her cabinet on a budget which they would never have agreed on as it cut Govt. spending and forced people to 'fend for themselves'.