Most businesses are closed on Sunday and national ("bank") holidays. Banks are open weekdays 9:30-4:30; offices are generally open 9:30-5:30.
The major national museums and galleries are open daily, with shorter hours on weekends than weekdays. Often they are open late one night a week.
The usual shop hours are Monday-Saturday 9-5:30 and Sunday noon-5. Around Oxford Street, Kensington High Street, and Knightsbridge, hours are 9:30-6, with late-night hours (until 7:30 or 8) on Wednesday or Thursday.