It has always baffled me why people bother to show ID when all one is required to give is their name and address. I personally would not like the idea of someone taking down details like my passport or driving licence number.
If an RPI has a reasonable suspicion that inaccurate, or false, details have been given, they will always ask for confirmation and that doesn't have to be something as formal as a driver's licence etc.
Neither do they HAVE to write down the details (although it might be good practice) simply confirming they have seen it and possibly recording nothing more than a serial number from passport (which only confirms name anyway) and perhaps say 'photo driver's licence confirmed a good likeness and the name & address given'.
There are a host of less formal items that can satisfy an inspector's request for confirmation of identity and if a traveller is on a railway without a valid ticket when they could have obtained one, or if any other offence is identified, National Railway Byelaw 23 (2005) makes a strict liability requirement that that person gives their details when asked.