You'd be surprised. Check out South West Trains' list of restrictions: National Rail's cycling guide (http://www.nationalrail.co.uk/passenger_services/cyclists.htm), A to B's summary of it (http://www.atob.org.uk/Bike_Rail.html). Half this problem arises because I live at Norbiton. It's extremely likely I'd be stopped from taking the trike on the train at the local station, let alone unloading it at Waterloo.