Geography 
The United Kingdom is an island located north of France, and inhabited by strange people : the British... oh, you already know that ? OK, so let's be a little more specific, we will focus on London.
London has 7,172,000 inhabitants, who live in some 1579 km². This is one of the biggest European cities in terms of population, with Paris, Moscow and Istanbul. But in fact it isn't really a city but a metropolitan area called Greater London (like the "Région Parisienne" in France). The Greater London administrative area comprises the City of London and 32 London boroughs (equivalent to French "cantons").
The London that most tourists see is Central London, which comprises the historic City of London, the West End, the City of Westminster, the Royal Borough of Kensington and Chelsea, which are the richest areas of London. In contrast, the East End has played host to successive waves of immigrants for centuries and contains some of the UK's most deprived areas.
Weather
That's the hard point. London's weather is nearly the same as Brittany or Normandy. Very cloudy, there is often rain and always wind. September is usually sunny, with temperatures about 15-20°C. But the remaining months are colder, with temperatures from 12-15° in October to 0-5° in December. In fact, the main problem is the wind, which cools you down a lot. Don't forget your warm clothes !

The other issue is about rain : sometimes it's raining permanently during one week. You'll probably need a good umbrella (and a strong one, British wind is definitely an umbrella killer) and waterproof shoes.
Time
London and the whole UK are under GMT time, and British have summer time like us. In fact, when it's 12:00 in Paris, it's always 11:00 in London, no matter of the summer time. That's easy, isn't it ?
Nonetheless, you will be hit by a small detail. Due to the timeshift and the latitude, the sunset comes very early : in December, the night falls by about 4:00 PM !
Now that you know in what you will put your toes into, let's have a look at formalities and things to prepare before you leave.
The London Survival Guide