It is an offence for someone under 18 years old to purchase or hire an air weapon, which includes some of the more powerful BB guns. It is also an offence if you are under 18 to sell, give or receive one of the weapons as a gift. This also covers the ammunition for the weapon.
Carrying an air weapon, and again this includes some BB guns, in a public place is an offence unless you have lawful authority or reasonable excuse.
It is an offence for anyone to fire an air weapon beyond the boundary of any premises without consent from the person whose land you are firing over or into. Remember this when practicing in your back garden. This carries a possible £1,000 fine.