I brought my iPhone from the U.S., turned off my U.S. phone number by calling my phone carrier in the U.S. and bought a U.K. sim card from a London phone store, which they inserted, into my iPhone. Make sure your iPhone is unlocked to do this. Once you have that sorted out, you can add minutes and date to your phone monthly. It's very easy. Just remember, you will no longer have access to your U.S. phone number when you do this. You can also purchase an inexpensive U.K. cell phone.
Phone Stores in London- Vodafone, Carphone Warehouse, 3 Store, O2
Make sure to have a debit card so you can take money out of ATM's. Also, it's good to have a credit card that does not charge foreign transaction fees on your purchases.
Dress for the rain! It rains often in London. I recommend bringing a warm raincoat, rain boots or waterproof boots, and a durable umbrella. It did not snow when I was there, and never got below 40 so I never needed a down jacket.
London fashion is classy and sophisticated, so dress to impress. If you want to fit in with the locals, I recommend bringing a pea coat, scarves, hats, and other classy/trendy clothing, but mostly neutral colors. They wear a lot of black, navy, and grey.
You will want to walk a lot in London because there's so much to see and you will become more familiar with the city. Make sure to bring comfortable walking shoes.
Bring a variety of clothing (layers) as the weather across Europe differs and you will probably want warmer clothing for Southern Europe- Italy, Spain, Greece, etc; and colder clothing for Eastern Europe- Prague, Germany, Switzerland, etc.
Primark! A great inexpensive store that has everything! Reminds me of Target. There is a huge Primark on Oxford Street. Closest tube stations: Holborn, Oxford Circus
Bring all of your medicine with you. If you need Advil, Benadryl, or other over the counter medication, bring them because they do not sell these in London. Also, bring gum if you chew gum, the gum brands are different in Europe.
Do not bother bringing. They will break since the European voltage is different from the U.S. and so I recommend purchasing in London.