You would need a better system than just using the current 4 character headcode as these are duplicated all over the country. A human could probably cope but a computer would be baffled. In data terms train IDs are already 6 characters, but then your train would be 1A00AA for example.
Most of mainland Europe uses individual train numbers that are visible to the public so it isn't a bad idea, but implementing it would require £,£££,£££s.
Meanwhile I'll check whether my plane next week has the flight number on the outside.