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