Are you talking about trains?
Yes on trains there are various railcards available which cost £30 per person and give 34% discounts for a year.
You need to make more than £30 in savings before they pay off. If you are a resident that is easy, for a tourist not so much so.
One is the Senior Railcard, available for over 65s.
The other is the 16-25 Railcard available to people of those ages and persons in full time education of any age with suitable documentation. Students, not teachers. The 16-25 Railcard also requires a photo.
You can't just hop on the train and claim the discount because of your age. You must buy the Railcard in a station or online (residents only).
Both Railcards carry peak time travel restrictions in and around London, and the 16-25 Railcard has morning restrictions nationwide except on weekends, bank holidays and in July and August.
Official information at http://www.nationalrail.co.uk/times_fares/46540.aspx