Byelaws are effectively local laws to deal with local issues. They are made by a body, such as a local authority, using powers granted by an Act of Parliament, and so are a form of delegated legislation.
The principal Act of Parliament governing the making and enforcement of byelaws is The Local Government Act 1972.
Local council byelaws are usually restricted to a particular place, e.g. a park, or a particular class of activities, such as tattooing.
Byelaws generally require something to be done - or not done - in a particular location. They are accompanied by a sanction or penalty for non-observance. Offences against byelaws attract a penalty fine which can, at present, only be enforced through the Magistrates' Court.
Historically councils were required to seek the Government's permission to make or revoke a byelaw. However the current Government has indicated that it will seek to change the law to enable local authorities to make and revoke byelaws without always requiring ministerial consent.
Oxford Byelaws (PDFs)