They are permitted on most trains but they must be in a carry bag/case (to prevent grease from the chain getting on other passengers' clothing).
They can generally NOT be taken on buses, and on the ones that do allow it, you may still be refused if the bus is crowded.
Most bus companies limit your luggage to 1meter (total of length/width/height) and 10 kg. For reference, a folded Brompton is 585mm X 565mm X 270mm for a total of 1420mm (1.42 meter)