One week London Itinerary with the kids.
The flight there...
I always suggest taking an overnight flight (if you are coming from east coast US area). It allows you to get a little shut eye on the flight (might not be the best sleep but at least it's something). You will arrive in the morning and will probably be exhausted, but DO NOT go to sleep. This will be your toughest day but believe me you're not going to want to take a nap. If you can stay up until at least 8/9:00pm, you will get a good night sleep and wake up without the trouble of jet-lag and be ready to start your vacation.
Now that JetBlue flies into London (Gatwick & Heathrow) from New York & Boston, this is my preferred method of transportation. Fairs are generally more reasonable and the airline is amazing.
Day 1: Arrival & Introduction to Central London
Arrive in London and settle into your accommodation. If your room isn't ready yet, most hotels allow you to store your bags while you explore the city. Take some time to explore the neighborhood. You want to get acquainted with the nearest tube stations as well as what restaurants and pubs are around you. Walking around with also help you to stay awake.
If you're hungry I suggest checking o ut a pub called The Prince Edward. Take a trip to the Diana Memorial Playground in Kensington Gardens. It's a great place to let the kids play and explore the pirate ship and other playground features. (and hopefully keep them awake a bit longer).
I suggest calling it an early night tonight. If you are hungry, try grabbing a quick bite at your hotel, or local pub. Then head back to your room for relaxation time. After a long day of travel it will be much needed and get you well rested for the remainder of your trip.
Day 2: Discovering History