Help with the difference between primary and private

[Tressalaea]

I currently live in the U.S.A., but I'm looking to move to the U.K. in the next 2 years or so. I'm trying to decide what would be better for my daughter (age 5 at the end of Aug), going regular primary or private, but I don't know much about private schools. I've read up a lot on primary schools, but I'm still trying to figure out what would be the better schools to pick.
The school my daughter is in currently teaches art, dance, and drama in addition to the regular curriculum, so I would like to get her into a school that teaches these things if possible. Preferrably anything within an hour outside London as I will likely be living in the Dagenham area or closer. Any suggestions would be greatly appreciated.

Thanks! :)