In legal practice, PUREX describes the solvent‑extraction method used in nuclear fuel reprocessing to separate uranium and plutonium from highly active fission products in spent nuclear fuel. The term is not defined in UK or Irish legislation or case law; it is a descriptive technical expression found in nuclear site licences, environmental permits, safety cases, decommissioning plans and commercial contracts. In the UK, PUREX was the process used at Sellafield’s THORP (Thermal Oxide Reprocessing Plant) until closure in 2018. Although commercial reprocessing has now ceased, PUREX remains relevant to legacy waste management, discharge authorisations, safeguards and allocation of liabilities. Key regulatory touchpoints include: nuclear site licensing by the Office for Nuclear Regulation under the Nuclear Installations Act 1965; radioactive substances permitting under the Environmental Permitting (England and Wales) Regulations 2016, the Environmental Authorisations (Scotland) Regulations 2018, and the Northern Ireland radioactive substances regime; and UK/IAEA safeguards for separated plutonium and uranium, and export‑control implications. In Ireland, there is no domestic reprocessing; PUREX mainly appears in policy, export control and international safeguards contexts (Euratom/IAEA), and transport and waste regulation. References to PUREX usually flag processes generating highly active liquid and vitrified high‑level waste, informing BAT/BPM assessments and storage and transport requirements.