This is a deal that's appeared in various forms before, but it's still really useful for a trip to London or somewhere else on the South West Trains network, like Bournemouth. I've had some really good days out using this offer :D
Its from Friday the 19th of May until the 14th of July, excluding 21 – 26 June (Glastonbury).
As usual, there's a few tweaks this time so it is worth reading the T&Cs,
there's restrictions on the times you can leave and arrive at London/Clapham Junction etc. and the time you can leave London/Clapham Junction etc. is slightly later than before. It's two pounds cheaper as well this time so four pounds per return cheaper. This ends in July which is different from previous years, but I expect there will be no offers during the massive works at Waterloo in August.
Another difference is that this time you can book on the day of travel, but allowing two hours for collection. I'm not sure if you can book in person, it doesn't make that clear but obviously online is fine.
Most of the big museums in London are free, and the big parks too like Hyde Park, Regent's Park etc., and you might be able to combine it with the 2-for-1 offer: http://www.hotukdeals.com/deals/2for1-loads-london-attractions-including-london-madam-tussauds-london-zoo-etc-with-2482495
You can see some of the most well-known sites in the world on a budget.
101 free things to do in London - http://www.visitlondon.com/things-to-do/budget-london/101-free-things-to-do-in-london
Download the CityMapper App for travelling around London.
Otherwise, Bournemouth is really nice for a sunny day on the beach with the kids.
South West Trains network map: https://www.southwesttrains.co.uk/plan-your-journey/network/
You can use their journey planner to see if your trip is eligible: https://buytickets.southwesttrains.co.uk/journey