Generally, businesses are closed on Sunday and national (bank) holidays. New Year's Day is a national holiday, but many major stores are open for the annual sales. Many restaurants are closed over the Christmas period.
Banks are open weekdays 9:30-4:30; offices are generally open 9:30-5:30.
Most gas stations in central London are open seven days, 24 hours. As you get farther out of town, and off trunk and major roads, hours vary considerably depending on the gas company, but are usually 8 AM-8 PM.
The major national museums and galleries are open daily, with shorter hours on weekends than weekdays. But there's a trend toward longer hours, such as one late-night opening a week.
Pharmacies, called chemists, are open, for the most part, Monday-Saturday 9:30 AM-5:30 PM. The leading chain drugstore, Boots, is open until 6 PM; the Oxford Street and Piccadilly Circus branches are also open Sunday and until 8 PM Thursday, and the Leicester Square branch stays open until 9 or later most nights. Bliss the Chemist at 5 Marble Arch has the longest opening hours, from 9 AM to midnight.
Shops and offices in central London tend to keep longer hours than those in the surrounding districts. The usual shop hours are Monday-Saturday 9 AM-5:30 PM. In the main shopping streets of Oxford Street, Kensington High Street, and Knightsbridge, hours are 9:30 AM-6 PM, with late-night opening hours in Oxford Street on Thursday until 7:30 or 8 PM, and in the latter areas on Wednesday. Many small general stores and newsagents stay open on Sunday; some chain and fashion stores in the tourist areas of Oxford Street and Piccadilly (and out-of-town shopping malls) also remain open.