[jamessb]

An offensive weapon is an article made, adapted or intended for causing injury.

Since a baseball bat is not made for causing injury, and is generally not adapted for this purpose (though it might be, e.g. by stacking nails into it), it would be necessary to show that it was possesed with the intention of causing injury. Note that posession for the purpose of 'self-defence' is not a legal defence.

Knives are different - it's an offense to possess a 'bladed' (excluding non-locking knives under 7.62 cm / 3 inches) or 'sharply pointed' article in a public place, even if there is no intent to cause harm, with certain exceptions (lawful authority, for use at work, religious reasons, or national costume).

[jwdunne]

I've seen police officers search for a ball when finding a baseball bat in someone's possession, implying that, without a ball, they consider it an offensive weapon.

This has been in the context of searches based on unrelated suspicions but the strong implication was there i.e "there better be a ball in the car to go with this".

Knives it's much more clear cut there. The baseball bat thing sticks out but to be honest, in the UK, a baseball bat may well be more commonly an offensive weapon than used for sport - the sport is no where near as popular.

I was going to add that I doubt officers would demand to see wickets and ball when finding a cricket bat.