The sale and use of fireworks in England and Wales are governed primarily by the Fireworks Regulations 2004 made under the Fireworks Act 2003. The law is basically the same in Scotland, where the 2004 Regulations also apply alongside the Fireworks (Scotland) Regulations 2004. The position is different in Northern Ireland, where a valid licence is needed to buy, possess and use fireworks (except indoor fireworks and sparklers).
More detail is given in a Commons Library Briefing:
Regulation of fireworks, Commons Library Briefing Paper CBP 5704, 6 November 2018.
A second Westminster Hall debate on the “Regulation and sale of fireworks” is scheduled for the following day, Tuesday 27 November 2018 at 2.30pm. The Member leading the debate is Alison Thewliss MP.