A good place to start is the National Rail Enquiries website
http://www.nationalrail.co.uk/
When your journey details appear in the journey planner, a cycle icon against a train indicates that the train operating company has a cycle policy. Click on this cycle and a couple of more clicks will take you to the cycle policy itself.
Most of the local/commuter trains have an area set aside for wheelchairs and cycles. This is usually indicated by a wheelchair and/or cycle picture on a plate on the outside by the nearest door (On most trains, it is in the centre carriage.
On some of the more long haul trains, there are special cycle racks in one of the carriages (You hang your bike from a couple of hooks in the cieling), and these companies have a maximum number of cycles policy and you are advised to book in advance. However, I have never seen these checked and have even wedged a third bike into the rack with no trouble and nothing said.
I have travelled from Stafford to Widney Manor with my bike for commuting (often at the extreme ends of rush hours) and have never hit problems (yet!).