Trains, Planes and automobiles

For overground, you can either take them on the carriage (on shorter lines), or you request a bike ticket, free of charge, which you affix to your cycle and then leave in a storage car at the front/back of the train.

absolutely do this at the same time as buying a ticket - saves a load of grief from (dare I say it) jobsworth train "managers" or whatever the hell they're called these days.