London is one of Europe's safest major cities. The main concerns are pickpocketing on the Tube (especially the Central and Jubilee lines), around Oxford Street, and at tourist attractions. Keep bags zipped and in front on crowded trains. Phone snatching (someone grabs your phone while you're using it and runs) has increased — be aware when using your phone on the street.
Most London neighborhoods are safe to walk at night. Exercise more caution in parts of Hackney, Peckham, and around Elephant and Castle late at night. The emergency number is 999 (or 112). The NHS provides free emergency treatment to all visitors. Tap water is safe everywhere.