Day trip via steam train rides from London?

Combine a visit to fairytale Bodiam Castle with a ride on Kent & East Sussex Railway.
http://kesr.org.uk
https://www.nationaltrust.org.uk/bodiam-castle

I don't think there are any steam railtours leaving London in early May. My suggestion is that you try some of the preserved railway locations within an easy day trip from London:

The Epping-Ongar Railway can be reached from central London on the London Underground.
The Bluebell Railway, by train from Victoria.
The Watercress Line by train from Waterloo.
The Didcot Railway Centre, by train from Paddington.

The KESR is a bit more difficult to reach from London by public transport as it has no connection to the main line railways.

Yes. Best with a car.

Here's a link to to the map of heritage railways: just click through to the websites of the individual railways. My own favourite since I used to live near it is the Bluebell Line. Frequen trains from London's Victoria Station to East Grinstead to access it.

Thanks for all your tips!

Click this link and scroll to May. I see on 6th May that a steam special will leave King’s Cross for York & Darlington. If you find a suitable trip - click the blue operator code on the right for details. Be warned: they can be expensive and are slower than the normal trains and are not really suitable for 3 year olds. http://www.uksteam.info/tours/trs17.htm#may

Most steam specials on the main line take all day, and would probably end up being boring for a three year old.

You might enjoy a visit to the London Transport Museum. It's in Covent Garden and your 3 year old might like pretending to drive the buses, etc.

Thanks for all the tips. Seems like many of the steam train rides are rather long. Does anyone know of a shorter ride that won't bore a 3-year-old?

Also, thanks mincepie for the tips on London Transport Museum, that looks like a good alternative.

David