The House of Commons is a democratically elected body comprised of 650 members (since 2010.) These 650 seats are filled by the following political parties:
1. Conservative and Unionist Party (referred to simply as the Conservative Party): 306 seats
2. labour Party: 258 seats
3. Liberal Democrats: 57 seats
4. Democratic Unionist Party: 8 seats
5. Scottish National Party: 6 seats
6. Sinn Fein: 4 seats (unseated, as they choose not to swear allegiance to the crown)
7. Plaid Cymru: 3 seats
8. Social Democratic and Labour Party: 3 seats
9. Alliance Party of Northern Ireland: 1 seat
10. Green Party of England and Wales: 1 seat
There are six other major organized parties which currently hold no seats. There are many other registered parties. The number changes often.
The above information comes from Wikipedia. The totals come out to only 647, but that's what they show.
There are a total of 419 registered parties in the UK as of 10 June, 2011.
This info only pertains to the parliament of the UK. Individual countries also have a parliament or an assembly, often with additional parties than those shown above.
Organized chaos? Not really. Not organized at all.
[Next: what these parties stand for, or say they stand for.]