There is no English Parliament (although there are devolved parliaments for Scotland, Wales and Northern Ireland).
The United Kingdom Parliament is currently made up of:
Conservative
Labour
Liberal Democrat
Democratic Unionist Party (of Northern Ireland)
Scottish National Party
Sinn Fein (of Northern Ireland)
Plaid Cymru (Welsh National Party)
Social Democratic and Labour Party (of Northern Ireland)
Green Party
Alliance Party (of Northern Ireland)
There are other political parties in the UK which stood for election to Parliament but won no seats, for example:
United Kingdom Independence Party
British National Party
National Front
Monster Raving Loony (William Hill) Party
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king or queen and Parliament
Roundheads
English nobles structured Parliament because they wanted justice in England.
became a permanent part of English government.
There is no such thing as the "English parliament" The Lower House of the United Kingdom Parliament is called the House of Commons.