Clean Air Act
The UK's Industrial Revolution in the 18th and 19th centuries was powered by coal and factories were often very near, or in , the cities. Coal burning in the home on stoves and fireplaces was also very common for heating. Air pollution was often very great and when it was foggy pollution levels rose and 'Smogs' were formed bringing cities to a standstill and causing many deaths.
Legislative controls on industrial emissions helped somewhat, but people were still burning a lot of coal on multifuel stoves and fireplaces for domestic heating.
After the Great London Smog of 1952 killed around 4,000 people the Clean Air Acts of 1956 and 1968 were introduced. These gave local authorities powers to control emissions of smoke and to declare Smoke Control Areas where burning fuel that produces smoke is banned. Many towns and cities now have smoke control areas especially in city centres and they have been effective in controlling the levels of smoke.
You are not allowed to burn fuel that emits smoke in a smoke control area either in a stove or fireplace. You are permitted to burn smokeless fuels on multifuel stoves and fireplaces
If in doubt contact your local authority. They can tell you if you are in a smoke control area and will have details of permitted fuels and appliances.