BB guns which fire plastic or aluminium balls by different methods such as compressed air or an electrical system may or may not be firearms and so may or may not be prohibited.
The soft air type of gun which is 'toy like' though it may be a little too powerful to be officially classed as a toy does not fit within the definition of a of a section 1 firearm because it is usually too low powered and is probably designed to fire plastic/aluminium balls
However, there are more powerful BB guns which could be considered firearms, for which, possession, purchase or acquisition, without holding a valid firearms certificate is an offence.
Possession of a BB guns that looks like a real firearm in a public place will amount to an offence of possession of an imitation firearm, regardless of the power of the gun itself. See Q329 for more information about imitation firearms.
(See Q326 regarding the exemption from holding a section 1 firearms certificate for airsoft guns).
If you are unsure whether your BB gun is legal or not, you should check with your local police force's firearms department who will be able to advise you.
Please note that all calls to police involving firearms are treated as if it is a genuine firearm so be aware that if you do wave an imitation firearm around you could find yourself surrounded by firearms officers pointing real weapons at you.