I think there's some confusion in terminology here.
'Route number' is usually considered to be the thing the public see (as in route 11 bus to Victoria) in which case the route numbers for Tramlink are 1 to 4.
That having been said, in London County Council / London Transport Tramways days, this was known as the 'service' number.
Vehicles in service will have some sort of number by which that vehicle's diagram / schedule is known. These aren't often visible to the public - most London buses have a 'running number' (e.g. SW 301 is the running number of a bus running from Stockwell Garage on route 11), London Underground trains have a train number that's visible on the front. (That being the working that particular train unit is allocated to that day) Traditionally, London tram staff did call this the 'route number'
and from memory, I think Blackpool and a few other northern corporations followed the same service / route number convention that London's trams did as well.
Then each crew or driver will also have their own duty number - in most cases, this will also not be visible to the public, and there are usually more driver duties than vehicles, and a driver will usually work 2 or more vehicles in the course of a day's shift.
I think what's on display on Croydon trams is probably the vehicle's working number but it could be the driver's duty number.
London Underground working timetables are now considered public domain (
here) - the train number and in some cases the driver duty number can be seen in them.
Tramlink working timetables are not considered public domain (correspondence
here)
The same arguments (private sector contractors) for not releasing Tramlink info could equally be applied to London Buses, but TfL have made the decision to release these -
here.