I used to be an 'appointed officer' with powers to enforce bits of national legislation and local bye-laws. I didn't have the power of arrest, but had very extensive powers of investigation and powers of entry. For instance I could demand to enter any commercial premises without a warrant. However, I never 'threw my weight around' unless the circumstances required it.
THE RCO will be an 'appointed officer' for the railway and its bye-laws.
The OP was on railway premises and had completed their journey. They therefore had no legal 'right' to remain on railway premises, an appointed officer of the railways then asked the OP for their name and address. The OP refused to give those details. Failure to give name and address to an appointed officer is obstruction....which is an offence, an arrestable offence. The RCO can't arrest you, but a BTP officer can. If I had been the officer I would have gone into full 'PACE' (Police and Criminal Evidence Act) mode. I would have informed the OP that failure to provide the personal details was an offence of obstruction, then cautioned them ( you are not obliged to say anything, etc), then asked for the details again. The caution also says that you are not under arrest, and are free to leave at any time...which the OP did....but an arrestable offence had been committed.
By what you've described and the terminology used it doesn't sound as though you were an 'accredited person' under the Railway Safety Accreditation Scheme, and whilst the legal environment in which you were operating would be similar, not all of the things you have listed in there are correct in a railway context.
Any member of rail staff in the course of their duties or a police officer (termed an 'authorised person') can enforce the byelaws, it does not need to be an 'appointed officer', this terminology does not exist in railway law so far as I am aware. Whilst there may be no legal right to remain on railway premises, there is equally no legal prohibition on someone remaining on railway premises except in certain circumstances such as being in non-public areas or causing a nuisance. They could be going to purchase a ticket, or use station facilities, for instance, neither of which are offences.
An accredited person under RSAS can request name and address under the railway byelaws, if they
reasonably suspect a person has breached the byelaws (which do create an offence of failing to give details, however the authorised person must tell the alleged offender the nature of the suspected byelaw breach and provide some form of identification) or under the RSAS regs, which along with the details of their individual accreditation state the offences which they are able to request name and address for. The accredited person under the RSAS regs must have
reason to believe that the offence has taken place.
It seems sensible to consider things in these cases from the point of a magistrate (who are ordinary people like you or I) hearing the case; if the defendant was stood up in court and said, "yer 'onner, I didn't give my details because the bloke walked up to me, didn't identify himself or who he represented, I hadn't broken the law and he didn't explain what I was supposed to have done then he told me I didn't have to say anything in case it harmed my defence in court so I walked off", I fear it would make it somewhat challenging for the prosecution to prove beyond reasonable doubt that an offence has been committed.