According to the BBC. no. The EU does not impose passport color restrictions on any member states and several states do not in fact have a burgundy passport.
The EU has mandated several wording and content changes to assist in freedom of movement for EU citizens and as this Guardian article (soft paywall) notes, most of the changes to size, biometrics and other security features are EU regulations passed in order to comply with US and ICAO regulations. If UK passport holders want to enjoy ease of travel around the world they'll still have to keep those parts.
Finally a Wikipedia link on Passports of the European Union.