Giving an officer of the Railway a false name is an Offence as I think you now realise.
It is specifically covered in the Regulation of the Railways Act S5.3.c
5 Penalty for avoiding payment of fare..
(1)Every passenger by a railway shall, on request by an officer or servant of a railway company, either produce, and if so requested deliver up, a ticket showing that his fare is paid, or pay his fare from the place whence he started, or give the officer or servant his name and address; and in case of default shall be liable on summary conviction to a fine not exceeding level 2 on the standard scale.
(2)If a passenger having failed either to produce, or if requested to deliver up, a ticket showing that his fare is paid, or to pay his fare, refuses or fails on request by an officer or servant of a railway company, to give his name and address, any officer of the company F8. . . may detain him until he can be conveniently brought before some justice or otherwise discharged by due course of law..
(3)If any person—.
- (a)Travels or attempts to travel on a railway without having previously paid his fare, and with intent to avoid payment thereof; or.
- (b)Having paid his fare for a certain distance, knowingly and wilfully proceeds by train beyond that distance without previously paying the additional fare for the additional distance, and with intent to avoid payment thereof; or.
- (c)Having failed to pay his fare, gives in reply to a request by an officer of a railway company a false name or address,.
he shall be liable on summary conviction to a fine not exceeding level 3 on the standard scale, or, in the case of a second or subsequent offence, either to a fine not exceeding level 3 on the standard scale, or in the discretion of the court to imprisonment for a term not exceeding three months.
[the phrase "on summary conviction" referring to a successful prosecution in the Magistrates' Court, where all evidence can be tested by cross-examination, which is one reason for NOT walking straight over there and confessing to all without legal guidance]
Whether the Railway Operator will invest the time required to pursue that, or the original ticket irregularity that led to the questionning, we can only guess.
However, for your false statement to be used as a factor in any attempted prosecution against you will depend on the precise details of how you were questionned and informed of the questionning - precise details which you haven't supplied but which are, broadly, as outlined in the Guidance to evidence gathering interviews under PACE (Police and Criminal Evidence Act).
I suspect that the Company is likely to investigate the apparent travel without a valid ticket and may, in the course of that investigation, realise that there is something wrong with your name and/or address. How they proceed at that point will be a combination of pragmatics and principle for them. Their pursuit of an apparent 'wrong ticket' is perhaps more likely to become more intense on discovering the false name and address.
I would never advise anyone to wait in the hope that they are not 'discovered' unless they have an extraordinaryily good reason to believe that their offence will remain undetected, and even then, I would struggle to find it 'advisable' to remain silent after such a deceit (though I'm sure many offenders do just that and their offence remains un-prosecuted).
On the otherhand, by walking into their offices and confessing to this offence is likely to be costly (the typical fines would be 'discounted' by your confession). Due to the costs involved, you would to well to be accompanied and represented by a lawyer, and for once, I'm not about to bemoan the shortage of lawyers specialising in Railway Law, because in this matter, any local Criminal lawyer should be on familiar ground other than the remark above about the Inspector's questionning probably NOT being to the standards required by PACE).