I am unsure where to post this, as it might be a normal price or a bug (I don't take the train much)
National Express East Coast currently sells train tickets from london - brighton for this summer are at £3 each way.
What is weird is that the nationalrail website price them at £5, but that none of the 14 other train operators has these tickets at £5 (their cheapest is £13 or so).
It might be the same for other south-east or national destinations, but I don't have the time to try. If you try, give us feedback ;-)
So, if like me you're planning a couple of days in Brighton this summer, enjoy!
edit 1: be sure to select 'London Victoria' not 'London (all)'
edit2: also works for Portsmouth and other stations in the south east. Thanks pompeyrich for testing!