Isn't that route sometimes a Great Northern service, Peterborough to Horsham train? They aren't as good at marking the carriages (if I recall, there is sometimes a grey wheelchair symbol on a grey (!) background on the appropriate carriage). But I've never had a problem putting a bike on those trains, admittedly north of London, + most of the doors have somewhere you can lean, on the luggage racks or in the standing space.
Isn't that route sometimes a Great Northern service, Peterborough to Horsham train? They aren't as good at marking the carriages (if I recall, there is sometimes a grey wheelchair symbol on a grey (!) background on the appropriate carriage). But I've never had a problem putting a bike on those trains, admittedly north of London, + most of the doors have somewhere you can lean, on the luggage racks or in the standing space.