I used to live in London.The week before Christmas Day is reallly busy. Like
@Dimplenose said it is dark by 4pm BUT the shops in the West End, Oxford Street / Regent Street/ Leiscester Square/ Covent Garden stay open until 8pm. Shopping Malls like the two huge Westfields, one in Shephards Bush and the other near The Olympic Park will be open until around 8pm too.
There is usually a Winter Wonderland outdoor Market / Fairground in Hyde Park, at the Green Park / Hyde Park Corner/ Park Lane / Marble Arch side.
The famous West End Theatre Shows, like Les Mis, Phantom of The Opera etc will have performances this week, but the theatres may be closed or have limited performance times from December 25 to January 2. You will have to research this.
The same with Museums and attractions like Madame Tussards, The London Dungeon etc They will be open as normal before December 25 but may be closed or have limited opening times from December 25 to January 2.
Christmas Eve the shops will be manic, as people finish work and do last minute Christmas Shopping.
There are usually some special Christmas events on too, which you will have to research. One year I went with my family to a special performance of Handels Messiah in St Martens In The Fields Church, which is at Trafalgar Square.
Christmas Day and the following day, called Boxing Day the streets will be empty, most places closed (including alot of restaurants) and the public transport will be very unreliable.
When it rains, London can very dreary and it chills you to the bone, even though the temperatures are only about 0 or -1c. This is because of the dampness and wind.
After Boxing Day, the days between Christmas and New Year will be a great time to visit. All the shops and places will open back up again but there wont be the huge crowds like Christmas week. This is because a huge number of people who live and work in London are not actually FROM London and they go home to their families over Christmas.
The New Year Fireworks to ring in the new year are world famous in London. Over half a million people will line the banks of the Thames to watch the 7 minute display. It is a free event but to control crowds it is a ticketed event. Public transport after the fireworks between midnight and 3am is usually free, so that everyone can get home.
New Years Day there is a parade through central London which is very popular with families. New Years Day will be like a Sunday, with limited shops open and limited public transport.
) but gets colder in January. It is often wet and being in the south of the country we seldom gets snow - but when we do get snow the transport systems don't cope well.
