Don't know much about other stuff but from what I experienced in England (London area especially), the public transport is unbelievably expensive. I went there for 2 weeks and maybe the biggest part of my expenses was spent on trains/buses/the tube. Especially trains.
This from the point of view of a tourist, though. I guess English citizens have some preferences/reductions?
No particular reductions, though there are a few railcards for certain groups (e.g. <25s, retired) that generally offer a 33% discount. The best way to save money on trains is just to know your way around the labyrinthine system. For example, if you're going to Birmingham, don't catch the crazily expensive Virgin service from Euston; take the London Midland semi-fast, or the Chiltern line from Marylebone.
You use an Oyster card in London and you buy train tickets in advance and after peak hours or arriving to less "main" train stations (like Liverpool Street instead of King's Cross). If you can, you take a National Express/Megabus coach. English, British doesn't matter unless you are an OAP.
This from the point of view of a tourist, though. I guess English citizens have some preferences/reductions?