The UK is very safe for tourists. London, despite its size, has relatively low violent crime compared to many world cities. The main concern in tourist areas is pickpocketing, particularly on the Tube, around Oxford Street, and at major attractions.
UK hospitals (NHS) provide free emergency treatment to all visitors. The emergency number is 999 (or 112). Tap water is safe everywhere. Political demonstrations are common but generally peaceful. Northern Ireland has been stable for years, though occasional tensions arise around marching season (July).