Registration, not a national licence
In England and Wales, both the person and the premises must be registered with the local authority for 'skin piercing / tattooing / semi-permanent skin colouring', and must comply with the council's byelaws on hygiene and cleanliness. Environmental Health officers inspect. London operates a similar scheme under the London Local Authorities Act 1991. Scotland licenses skin-piercing and tattooing under the Civic Government (Scotland) Act; Northern Ireland under its own 2020 scheme.
Age and pigments
It is an offence to tattoo a person under 18 in the UK. Pigments must meet the retained UK REACH rules on substances in tattoo and permanent-makeup inks (mirroring the EU restriction, with a UK-specific list); use only compliant, fully disclosed products and keep the documentation.
Other duties
Insurance is expected by councils and landlords; a sharps/clinical-waste contract is required; and advertising must comply with ASA/CAP rules — misleading before/after imagery and unqualified 'safe/permanent' claims can be challenged.