This depends on whether you are asking about actual serious political parties. There are so many supposed "parties" that run a candidate or two but who are in no way serious.
In terms of parties that have relevance, there are only 4 political parties that have nationwide followings and were able to win at least one seat in the House of Commons in the last election. These parties were
- The Conservatives (Tories)
- The Liberal-Democrats
- The Green Party
There are a few other parties that are nationalist parties and therefore don't have much of a following outside of their own areas.
As far as the total number of parties that are registered with the government, one recent count puts the number at 392 parties that are officially registered, including Independent.
There are approximately 18 political parties in the United Kingdom today, such as Labour and Independent.