You are coming to London and you have to organize your life here?
1. Passport / Identity Card
Make sure your passport is valid. If you are German: Get a valid Personalausweis as well as a valid Reisepass and take both with you. Store them at two different locations (for example: 1. body 2. apartment). If you have children ensure that their passports include official pictures.
2. Get a health insurance.
3. Get a bank account
Not easy! Without an official address you won't get a bank account but without a bank account you will not get an apartment, either. How it worked for me: Collect a nice amount of money onto your foreign account, change your address of your foreign account to the address of a friend who already lives in London, let your foreign bank send you a bank statement to this address, take this statement to a London bank and open your new account.
4. Get an annual ticket for London Underground
I purchased an annual ticket ("golden ticket") for zones 1 through 4. Do NOT waste your money on an Oyster card. It's a rip-off. With your golden ticket you can buy long distance tickets cheaper as well. You will need a passport photograph for your customer card.
5. Get a frequent flyer card for all airlines you use
... and book your flights as early as possible (more than two months in advance). Check in online 24 hours before departure. Try to travel without hold baggage.
6. Get a credit card
Makes life easier in London. Two are better than one if a card will not be accepted and if you like to differentiate between private and business payments.