If you have an Oyster card or a Freedom pass, between 26 June and 25 July, you can get cheap off peak return tickets from London Mainline stations to a few different places for between £5 and £20. eg
£5 return: Brighton, Bognor Regis, Eastbourne, Littlehampton or Southend-on-Sea.
£5 return: Arundel, Chichester, Dorking or Windsor.
£10 return: Oxford or Cambridge.
£15 return: Salisbury, Stratford-upon-Avon or Winchester .
£15 return: Birmingham, Liverpool or Southampton.
£20 return: Bournemouth, Bristol, Cardiff or Norwich.
Each adult needs to have an Oyster card, or a Freedom pass and have a voucher that you print from the WWW site.
You can only get the tickets from London travelling out - and back. You couldn't use it to go from Brighton-London-Brighton.