To date there has been 53 of what we would recognise as Prime Ministers, 52 men and 1 woman (Margaret Thatcher). Each holder of this office has wielded their responsibilities differently and each has taken a slightly different role. These have mainly been defined by the Prime Minister themselves.
The Role of a Prime Minister is to be the First Minister of State; they are in theory the Queens chief advisor; however they are now in fact the Head of Government and are the ones who exercise the power to govern. They are the leading authority of Government. Although the Prime Minister is the Head of Government he is still accountable to Parliament and his power comes from Parliamentary Sovereignty, this is called a Parliamentary System.
Some have compared them to a President but there are some problems with this comparison.
Below is a table showing the two different styles Presidential (link in the USA) and our system Parliamentary.
Prime Minister is technically appointed by the Monarch and therefore carries her authority (royal prerogative). In practice, appointment by the Queen is just a formality as there is usually a majority party with an undisputed leader
Usually the Prime Minister if the leader of the majority party in the HOC (except with coalitions such as the newly formed Con-Lib coalition)
The PM must maintain the support of their party to remain the PM – Margaret Thatcher was removed as leader by her own party – failed to support her when challenged by Michael Heseltine.
Under the coalitions the PM needs the support of both parties/
Needs the support of the majority of the HOC. It is backbench MPs who can bring down a government in a Vote of No confidence (e.g. James Callaghan in 1979), forcing the PM to dissolve Parliament
Voters have been shown in recent years to be increasingly influenced by the standing of party leaders therefore the winning party can claim the authority of the people. People vote on image of party leaders rather than policy which puts PM in a powerful position over other MPs and ministers – their position in government is dependent on the party leader
On the next page you will find this section summed up.