Am I British?

[kera]

I was born in 1996. My father was British by naturalization and my mother a Jamaican at the time of my birth and were never married nor did they get married later on. Am I a British citizen due to this? If so, is there any application or whatsoever that I would need to do to verify my citizenship or should I just apply for a British passport?
Also, would I be able to live and work in the UK without any other formality?

 

[Riley Haas]

Yes, you're British, but you will have to register as a British citizen: https://www.immigroup.com/registration-british-citizen

Once you are registered, you can apply for your passport.

Once you have your passport, you can move to the UK without doing anything else.