The offense according to the Offensive Weapons Act 1996 is that of "carrying an offensive weapon without lawful authority or reasonable excuse". To the best of my knowledge, a person can carry any item which could be used as a weapon if that item would be a reasonable or normal item for that person to carry, a tool of the trade. I've probably butchered it horribly but the upshot is that a plumber could reasonably carry a pipe wrench, a carpenter a hammer, and so on. Police-style batons are restricted for use by police. Since an offensive weapon is defined in law as "any object that has been made or adapted to cause injury" and includes "an object not designed to hurt anyone, but you're carrying it round intending to cause injury, like nail scissors", then carrying a baseball bat for the purpose of using it as a weapon is definitely illegal. It's no defense to say that you're only carrying it for self-defense.
At the age of five, Skagra decided emphatically that God did not exist. This revelation tends to make most people in the universe who have it react in one of two ways - with relief or with despair. Only Skagra responded to it by thinking, 'Wait a second. That means there's a situation vacant.'