London has a great system of public transit. Transport for London is the agency that manages public transit, which includes London's buses, tubes, and trains.
The city is divided into 9 transit zones that radiate out from the city center, with Zone 1 in the middle and Zone 9 at the outer edge of the city. Costs for public transport depend on which transit zones you start and end in.
Travel is managed through the Oyster card which you swipe at a turnstile to enter and exit train stations and buses. You can pay as you go or get weekly, monthly, or annual discounts if you'll be commuting to the same location each week. Each duration offers a different discount level, with longer durations (i.e. an annual pass) offering the largest discount. An annual pass can range from £972 all the way up to £3,048 depending which zones you're traveling to and from.
Owning a car in London is certainly not necessary in most parts of the city and many recommend against it: traffic is horrible, parking is difficult, and an £11.50 congestion fee is charged for any vehicles entering central London during business hours on Monday-Friday.
With that said, there are some parts of the city farther out from the center that don't have great public transit options where a car will make life easier.
TRANSIT AND WALKABILITY RATINGS
For each London neighborhood you'll see a Transit rating and a Walkability rating. The Transit rating tells you how good and reliable public transportation options are in that neighborhood. The Walkability rating tells you how many local amenities (shops, restaurants, fitness options, etc.) you can walk to in that neighborhood.