1-The correct chronological order of the Prime Ministers listed, along with their dates in power and main political ideas, is as follows:

Clement Attlee: Prime Minister from 1945 to 1951. He was the leader of the Labour Party and his main political idea was the establishment of a welfare state, with policies focused on social reform, nationalization of key industries, and the creation of the National Health Service (NHS).

Margaret Thatcher: Prime Minister from 1979 to 1990. She was the leader of the Conservative Party and her main political ideas were centered around free-market capitalism, privatization of state-owned industries, and reduction of the role of the state in the economy. She was known for her conservative and neoliberal policies.

Tony Blair: Prime Minister from 1997 to 2007. He was the leader of the Labour Party and his main political ideas were centered around "New Labour" ideology, which combined elements of social democracy with market-oriented policies. He focused on modernization, economic growth, and social welfare reforms.

David Cameron: Prime Minister from 2010 to 2016. He was the leader of the Conservative Party and his main political ideas were centered around modernizing the Conservative Party, advocating for social and economic reforms, and promoting a "Big Society" agenda which emphasized community involvement and social responsibility.

Theresa May: Prime Minister from 2016 to 2019. She was the leader of the Conservative Party and her main political ideas were centered around Brexit and managing the process of the United Kingdom leaving the European Union, as well as focusing on social issues such as mental health and social mobility.

2-Yes, the different branches of power are separated in the British political system. The British political system follows the principle of the separation of powers, which means that the powers of government are divided among different branches: the legislative branch (Parliament), the executive branch (government), and the judiciary (courts). This separation of powers is aimed at ensuring a system of checks and balances, where each branch has distinct roles and responsibilities, and they operate independently of each other to prevent the concentration of power in one branch.

3-The expression "a monarch who reigns but does not rule" refers to a situation where a monarch holds a ceremonial or symbolic position of power, but does not have real governing authority or control over the government's decision-making process. In a constitutional monarchy like the United Kingdom, the monarch's role is largely symbolic, with limited or no involvement in the day-to-day affairs of the government. The actual governing authority is vested in the elected representatives of the people, such as the Prime Minister and the Parliament.

4-The "Good Friday Agreement" is a peace agreement reached in 1998 between the governments of the United Kingdom and the Republic of Ireland, as well as most of the political parties in Northern Ireland, to address the sectarian conflict known as "The Troubles". It aimed to establish a power-sharing government in Northern Ireland, promote equality, and respect for human rights, and provide a framework for reconciliation between the nationalist and unionist communities.

5-The impact of Brexit on the Union, which includes the United Kingdom of Great Britain and Northern Ireland, has been significant. It has led to increased calls for Scottish independence due to Scotland's preference to remain in the EU, raised concerns about the border between Northern Ireland and the Republic of Ireland, and highlighted economic concerns in Wales. The potential for the United Kingdom to break up due to these tensions and differences remains uncertain and will depend on various political, economic, and social factors in the future.