They did this same deal for a limited time a few months ago offering 50% off when you book your off peak train ticket online with kids traveling for 50p.
Its not on every journey though and the deal ends on the 11th April.
Copied and pasted from southernrail.com
Great News. You can now save a massive 50% when travelling off-peak, simply by booking your ticket online.
Our half price offer is now available on Off-Peak Day tickets for a limited period only Special Offer ends 11th April so book today.
All you need to do is book online, itll take a few clicks and you wont pay a penny extra for booking fees, credit charges or postage. Just decide when and where you want to travel and click below to get your tickets half price today.
Ive just saved £20 on my easter travel plans. Hope this helps someone.