Retailers must only sell fireworks that conform to British Safety Standards and meet certain noise conditions. They must have BS 7114 printed on the box. Unless they have a special license, suppliers must only sell fireworks during the weeks leading up to Bonfire Night, New Year's Eve, Diwali and Chinese New Year.
According to regulations made under the Fireworks Act 2003, it is an offence for under 18s to possess fireworks in a public place and for anyone to let fireworks off during night hours (11pm to 7am). The only exemptions to this law are on 5 November when you can set them off until midnight and New Year's Eve, Chinese New Year and Diwali when they can be set off until 1am.
Enforcement rests with the police who have the power to issue penalty notices of £80.
It is also an offence under section 80 of the Explosives Act 1875 to throw or set off fireworks in any highway, street, thoroughfare or public place. The power to enforce this section of the Act also rests with the police.
It is very unlikely that fireworks noise will ever be frequent enough from any particular premises to constitute a statutory nuisance.