You'll find plenty to do and see, have no fear.

If you will be living in Surrey, you'll be able to catch a train with your son (cheaper at weekends), go to central London, and just for one idea, head over towards Kensington.

Natural History Museum
Science Museum
V&A Museum (Victoria & Albert)
British Museum

You could spend hours in each one of those, and they are all free.

Numerous parks, changing the guard, do a visit around the houses of parliament, big ben

Believe me, plenty to do, that doesn't cost the earth

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