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 BB 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 section 1 firearm because it is usually too low powered and is probably designed to fire plastic/aluminium pellets. It will normally have a very low power rating, compared to an average air weapon.
An air weapon is powerful enough to injure and kill in the right circumstances, and, does therefore fit within the definition of a firearm (but is not normally powerful enough to be a section 1 firearm See Q326 regarding the exemption from holding a section 1 firearms certificate for airsoft guns. The average air weapon is probably about 150 times more powerful than a 'toy like' soft BB gun.
If you are unsure whether your BB gun is legal or not, you should check with your police force's firearms department who will be able to advise you.
Given the nature of BB guns and their capabilities, it is not advisable to allow young children to be in possession of them.
Also be aware that many BB guns are extremely realistic and the police treat all reports involving weapons as if they are real live firearms.
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.