Some royal palaces or parts of the residences are open to public. They give a very good insight into the royal history and the present role of monarchy in Britain.
It is an active royal residence today, and has been such since 17th century. Queen Victoria, Princess Margaret (a sister of Queen Elizabeth II), and Princess Diana lived here. Prince William and Princess Kate live in Princess Margaret's apartment in Kensington Palace since 2013. Prince Harry also lives at Kensington Palace, as well as other members of the Royal Family. However their residences are not open and cannot be accessed by public.
Clarence House is the official residence of Prince Charles and Lady Camilla, the Duchess of Cornwall. Built in early 19th century, it is located on The Mall. The Mall is the road that goes from Trafalgar Square to Buckingham Palace.
Banqueting House is the only remaining part of the Palace of Whitehall which was the main residence of the English monarchs in 16th and 17th centuries. Banqueting House is open to public visits, it is very easy to get to it, and admission tickets are just £7 per adult. In addition to its classic architecture that set trends to many building in London and Britain, Banqueting House is famous for ceiling painting by Rubens, other works of art, including paintings and statues, and the place of execution of Charles I.
Hampton Court Palace is famous for being owned by King Henry VIII. No one lived in the palace since 18th century. It is now open to public throughout the year, and is a great opportunity for seeing the royal residence of Henry VIII and exploring its gardens. Things to see include the famous Tudor Kitchens - see how cooking was done for royals, for 600 people twice a day.