As a tube worker let me give you advice about transport.
If your 3yo is in a buggy well, only 40% of the tube system is step-free so use buses as much as you can. A lot of the big sights are walking distance anyway, so get an A-Z and plan a route. Also consult the TfL website on www.tfl.gov.uk.
If you have a family railcard you can get a discount on your one day travel card Zones 1-6. You only need 1-2 zones, and kids under 11 are free on transport in London, but if you pay for one of your children with the railcard you get more Zones and it costs less.
Don't buy an Oyster card, not worth it for one day and if you forget to touch in or out it charges £7.20.
Drum into your kids what they should do if they are separated from you. My daughter was told from the age of 3, stay where you are and I will come and find you. She also wears an identity bracelet when I know it will be busy in town. If on the underground there are help points and if your eldest gets separated from you drum into her to press the green emergency button. A female member of staff will be despatched to watch the kids and we do our best to reunite you.
Take a bag of snacks and a large bottle of water...the "locals" and "metros" are extortionate. One vendor tried to charge me £1.99 for a cornetto
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Final word on finding your way round... The best people to ask for help are police staff, taxi drivers, and people in shops. Bus drivers are grumpy, and as a tube worker, I can't say we are much better
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