This research paper provides an exhaustive critical inquiry into modern British public law, constitutional doctrine, and administrative adjudication. Focusing on the uncodified constitutional arrangement of the United Kingdom, the principle of Parliamentary Sovereignty, royal prerogative powers, and the Supreme Court of the United Kingdom (UKSC), this study evaluates how British legal institutions navigate post-Brexit regulatory realignment. Additionally, it investigates asymmetric devolution across Scotland, Wales, and Northern Ireland, human rights protection under the Human Rights Act 1998, judicial review boundaries, digital public administration, and international trade governance.