The Prime Minister also has massive powers of patronage over the Church of England (bishops etc), senior judges (Lord Chief Justice), Privy Councillors and even the Chairperson of the BBC. However this power has been gradually reduced— until very recently the PM appointed the Lord Chancellor and the top judges in the country— This has now been taken over by an Independent appointments body. Also, appointments such as Bishops and Chairperson of the BBC are often predetermined by other people in positions. The PM is often simply a rubber stamp.
Other aspects of patronage include giving knighthoods and peerages. Peers should be appointed to the House of Lords on basis of merit due to their service to the community. For example, Lord Sugar was appointed because of his service to business.
A second power he has is foreign policy; he can declare war on another country as well as annex territories. Examples include the Falklands War 1982 when Thatcher took the country to war with Argentina when they invaded the British Falkland Islands. She took all decisions with her inner war cabinet and she was in charge of the armed forces and all funds necessary. There was no vote required in the Commons. She also led the Diplomatic initiatives to try and obtain US and European public approval.
There was also the Gulf War 1990 John Major was the USA’s number one ally in removing Iraqi Forces from Kuwait after they had invaded. He once again committed troops and informed Parliament of his intentions.
There was also the 1991 Maastricht Treaty. This was a treaty which would bring the UK closer to Europe and was actually opposed by a majority of the Commons. John Major did not actually need the approval of the commons as he can sign treaties with Prerogative Powers. He called a vote anyway and told the commons that he would sign it regardless of the vote. The government won by threatening to resign and the conservative MPs voted with the PM rather than face their electorate. Queen theoretically could have intervened if he had lost the vote and signed the Treaty.
Blair called a vote on the war in Iraq in 2003. It had not been done before. He has perhaps now set a precedent on a PM taking the country to war in the future. John Major has perhaps also set a precedent on Treaties that have huge consequences for the country.
Although Prerogative Powers exist you would be foolish not to consult Parliament because if there is an error you could lose your job as Eden did with the Suez crisis in 1953.