would a 10 yr old with parents be able to do

Day 1:
Tower of London
Greenwich Med. Time
Churchill's Bunker
Natural History Museum

Day 2:
Changing of the Guards at Buckingham palace
Princess Diana's Playground
Hamley's Toy Shop

we will be walking and catching the tube if need be.

what do you think?

Day 1 seems like a lot, though I have not been to the last 2 places on your list for Day 1. There is a lot to see at the Tower and lines can be long, depending on the day and time of year. Get there first thing in the morning and see the crown jewels first, then link up with a yeoman warder tour. They are really funny guys and they play to the kids in the crown so your 10-yr-old should enjoy that. You may also want to tour the Tower Bridge, which is right next door.
When we took our kids to London I was told by several fodorites to skip the changing of the guards due to crowds and difficulty seeing much of anything unless you get there VERY early and stand around for a long time. Hamley' is fun. You didn't say if the 10-year-old is a boy or a girl. This may be a sexist suggestion, but a boy might enjoy the London transport museum (there's a simulator that will allow a kid to "drive" a tube train.) and a girl might enjoy the dress exhibit at the V&A.

I have to agree that Day 1 would be tough. You have picked four locations that are spread out throughout the city. Even with the tube it will be tough to get to all 4.

There is a lot to see at the Tower of London, and I agree with the suggestion of atleast walking across the Tower Bridge. Greenwich is a bit further out and would definitely want to take the time to explore a bit more.

You may want to consider the Natural History Museum on Day 2 as it is closer to Princess Diana's playground. I think it is doable to add to Day 2.

We didn't make it to Chruchill's Bunker but did go to the Imperial War Museum and really LOVED that.

Day 1 is impossible IMHO. (Tower of London for a 10 year old will be at least 4 hours. And it takes a while to get to and fro Greenwich - never mind all the way up that hill to the Prime Meridien. And are you going to ignore the Cutty Sark and the Maritime Museums?

Why not take at least one major item and add to day 2?

We took our daughter to London at 10 years old too and she loved it.
I think that you could easily do the Churchill War Rooms and Tower of London on day one...Then you need to do some kid time - London Eye - walk along the river...

Day 2 looks pretty easy.

Here are the things my daughter really enjoyed in London:
Westminster Abbey
Double Decker bus ride
Hamley's (She made a stuffed tiger)
Tower of London
Churchill War Rooms
Courtault Gallery (she loves Impressionism)
British Musueum (Rosetta Stone- She was studying about it in school)
Hampton Court
Day trip to Bath
Oxford Street
Carnaby Street
Covent Garden (shopping and the buskers)
Show (My Fair Lady)
Picadilly Circus
Tea at the Dorchester

I really need a map of London to pinpoint where everything is so I can sort of calculate our time.

Is a map available on the internet or fodor's?

My son.

thanks.

We had our 7 and 11 yr. (at the time) in London 3 years ago and only had a weekend so we did tower of london and one museum the first day (plus lion king at night) and then did everything on your day 2 plus the churchill bunker. That was plenty and the kids enjoyed it and no one was burnt out.

I did splurge and get a london pass because it allowed us to bypass the lines and the tower and after seeing the chaning of the guards, we ran into the queens mews and gallery since it was included in our pass and therefore free.

I highly recommed Mary Poppins, we saw that in london this past summer and the kids loved it.

Have fun and be prepared to spend some money in Hamley's.

Here's a pdf of main attractions and transport routes. Hope it helps!

http://www.tfl.gov.uk/tfl/pdfdocs/cen_bus.pdf

Forgot to add, bus routes only on the map above.

I think you should change day 2 and cover the main attractions in south Kensington on that day such as Natural History museum and Princess Diana Playground . Your child will also love the Science musem which is next door to the Natural History museum .
For day 1 you should decide whether you really want to go to Greenwich which is far out and I'm not sure you have time for this. Churchills bunker and Tower of London is too much for half a day, so pick one then spend a pleasant afternoon walking around Piccadilly, Regent Street, St James Street and then Hamleys!
Remember, London takes a while to get around so its best to focus on 2 areas in 2 days. Your 10 year old will enjoy most things as long as you don't try to do too much. enjoy!