The main prerogative powers exercised by the PM are:
1 Patronage:
Appointment of ministers, senior judges, Bishops, ambassadors, EU commissioners and members of quangos (non-elected governmental bodies). There are about 100 posts in the government from junior minister upwards and this payroll vote is a good disciplining factor for MPs generally. The prime minister is also able to recommend the award of honours to individuals, from peerages and knighthoods to MBEs. AS government's role has grown this century, so have the patronage powers of the PM. Some have suggested that ministerial and even judicial appointments be subject to parliamentary approval; Tony Benn for example has long argued for the Commons having the right to ratify cabinet appointees.
Dissolution.
A PM can in normal circumstances be expected to be granted a dissolution of parliament, ( the process for beginning a general election ).The threat of dissolution has been used by John Major, notably by making the social chapter vote on the Maastricht treaty a vote of confidence in 1992. This threat has limited use since it is a high risk strategy. The alternative to this would be fixed term parliaments as is the case in most other systems, or giving the powers of dissolution to some other body which would be difficult in the British system, since elsewhere that power is often held by a president.
Treaty signing and declaring war are also prerogative powers; John Major in 1992 suggested that he did not need parliamentary approval of the Maastricht treaty because of this power, but that would have been breaking with tradition. Whatever the merits of that particular case, it highlights a major problem of the current constitutional set up, namely, its reliance on convention and to some extent the good faith of the government.
Other powers: are the control that the PM has over the Cabinet system and Whitehall and those that derive from being a Party leader.
LIMITATIONS:
The Prime Minister does have many powers, but there are still some limitations which should be considered. The limit to these powers comes from the party he represents. .
If a Prime Minister loses the support from his party's back-benchers, his position becomes very weak. This happened to both Margaret Thatcher and John Major. In one speech made in the House of Commons, Geoffrey Howe, a former Cabinet colleague of Thatcher's, started the process that lead to an effective revolt against her style of leadership and her ultimate resignation as Prime Minister in 1990. John Major also experienced a revolt over his support for Britain developing greater links with Europe. He is alleged to have referred to those Cabinet colleagues who did not support his stance on Europe as "bastards". By 1997, when Major called a general election, the party was in such disarray that it suffered the biggest electoral defeat in recent history
Blair has to respect that his position as party leader is dependent on maintaining support amongst the Labour MP back-benchers. If he loses this, he will lose the authority required by a party leader and his hopes of leading the party without the support of that party will be minimal. As Prime Minister, such a position would be untenable. Those back-benchers who fail to support his style of leadership could put up a 'stalking horse' candidate in an election contest for party leadership. It is very damaging for the party as the start of any rebellion might prove difficult to contain and it might gain an unstoppable momentum. An authoritative leadership of the party is a vital component for the Prime Minister to be successful and the Prime Minister would always keep a close eye on what is said by his party's back-bench MP's
Another factor that limits a Prime Minister's power is the fact that he is seen to be publicly responsible for any major mishap that occurs during his time in power. When things go well, the Prime Minister can bath in the glory but the opposite is also true. As the most known member of the government, it is he that the public hold to be accountable when things go wrong. Anthony Eden was held responsible for the Suez episode in 1956; Edward Heath was seen as the person responsible for the 1974 miners strike when a three-day working week was introduced; Margaret Thatcher was held responsible for the problems associated with the Poll Tax etc. Tony Blair has been accused of being too friendly with America's President Bush and not being critical enough of the President's foreign policy designs.
Though the Prime Minister has a great deal of political power, this power is also balanced by the fact that there are limitations to that power. While a Prime Minister has the backing of his party, his position is secure; if he loses that support, then his position becomes very vulnerable. Any Prime Minister would always ensure that he knows what the opinions of the back-benchers are
References:
John Oakland: Contemporary Britain.
David Childs: Britain since 1939.
Anthony King: The British Prime Minister.