London is famous for its red double-decker buses - exploring the city by riding such a bus is a good choice. Don't consider a bus as an adequate transportation if you are traveling with luggage and kids. London also offers a large net of underground and overground trains. Some airports are reachable by overground, The so called Tube works well but avoid it during business hours. Taxis are to easily to hail everywhere. Uber is also available.
London Transportation services offers a contactless card system call Oyster. Oyster cards can be bought and topped up at most train and underground stations as well as at large convenient stores. Please be aware that you wont be able to pay a ticket for any public transportation in cash.