If your budget permits I would definitely recommend buying an open top bus tour of london. Rather than being underground, you get off wherever you want and you are not so tired with little ones. I did it a couple of years ago with a 4 month old baby an 4 year old and 7 year old and we had a wonderful time. You see so much, get off where you want and there is commentary throughout so even if you have been to london quite a bit, there is something for everyone. Stops off at hamleys.
It is quite expensive £25 per adult from memory but absolutly makes a wonderful day out. A cheaper option is to get a cab and ask the cabbie to take you via as many sites as possible and generally they will tell you where things are.
If you cannot stretch to this, I would definitely recommend the science museum as this makes a wonderful day out and is free to enter. There is an indoor picnic area and the interactive play areas in the basement and third floor are fantastic and will keep the kids busy all day. Dont try to do the sceince museum and natural history in one day as it is too much.
Avoid harrods toy department - it will cost you the earth and actually I didnt think that there was too much out of the ordinary (but we are lucky to have a really good toy shop in colchester). Stick to the food hall in harrods and the sweets - there are lots of samples and the food is to die for!
I had a wonderful time with my dd when she was 4. We went to watch changing of the guard (check before you go when it is on - google) and then we had a picnic in green park (next to the palace) and then we booked a tour around the palace which was brilliant. You also get to see the queens carriages etc. Really good day out. Then could get a taxi rid to harrods - not too far and back to the station.
Tower of london is good.
London eye lovely but expensive and my dds friend cried off (age 7) as she was too scared after I had paid for it.
Also, as she is older, if you write to your MP in advance you can get free tickets to go around the houses of parliament which is brilliant. You get to go inside the commons and house of lords it is a great day out.
Portrait gallery on trafalgar square is nice and there are lots of restaurants and cafes nearby. From there you can walk to the palace or down to big ben and the embankment (past downing street). If your legs are not too tired that is.
If you have tesco clubcard vouchers there are loads of things you can change them for in london and that custs the cost massively.
Finally if you are feeling rich get tickets to see the lion king. It is the best show ever!
Have a wonderful time (can I come?!!)