1. The British political system

2. The legislative power Parliament is made up of two Chambers:
The House of Lords (non-elected members = peers or peeresses)
It provides an independent, non-political check to the House of Commons and the government.
The House of Commons (elected for a maximum of 5 years)
Members of Parliament discuss and vote on new legislation and control the executive (the ministers).

3. The executive power
The Prime Minister (the PM) = the leader of the party with the largest number of votes (General Elections)
The Cabinet = the PM + some 20 senior ministers
Some important members:
The Deputy Prime Minister
The Chancellor of the Exchequer
The Lord Chancellor
The Foreign Secretary
The Home Secretary

4. Parties Two main parties:
The Conservative Party (Tory Party) – right-wing liberal* policies
The Labour Party – traditionally the party of the working class
Third party: the Liberal Democrat Party – more liberal, pro-European and in favour of constitutional reform
Some other parties:
Plaid Cymru /ˌplaɪd ˈkʌm.ri/ (Welsh nationalist party)
The SNP (Scottish National Party)
The DUP (the Irish Democratic Unionist Party)
The BNP (the British National Party – extreme right-wing)
The Communist Party

5. Liberal - definitions Cambridge dictionary
UK: believing in or allowing more personal freedom and development towards a fairer sharing of wealth and power within society
US: tending to emphasize the need to make new laws when necessary because of changing conditions and to depend on the government to provide social services
Oxford dictionary
 favouring individual liberty, free trade, and moderate political and social reform.
Libertarian
(Cambridge dictionary): a person who believes that people should be free to think and behave as they want and should not have limits put on them by governments
To go further:

6. The notion of liberalism
Liberalism considers individuals to be the seat of moral value and each individual as of equal worth. Hence, the individual should be free to choose his or her own ends in life. Liberalism is morally neutral in regards to the ends people choose for themselves, but it is not morally neutral in its view that such individual choice is desirable and must be safeguarded from unwarranted interference from the state.