What are the restrictions/rules on travelling with an air-rifle in England via train/bus?

Sorry you've had to listen to the above negativity. Obviously you are a responsible airgunner. Presently the law says that to have an air rifle in public it must be cased and unloaded. Unloaded means no pellet in the breech whether ******/charged or not. Thus you would be ok to have a cased airrifle (unloaded) on public transport. It may be wise to carry I.d. in case of encountering an over zealous official.....maybe a club membership card. Good luck at the shoot and nice rifle!!