Additionally, section 3 (1) of the Criminal Law Act 1967 gives any person a right to use such force as is reasonable in the circumstances for prevention of crime, the crime in this case being the failure to provide details when suspected of a ticketing violation.
The word "reasonable" is rather crucial here. Hence why I, a civilian, cannot use force against someone who is committing such crimes as jaywalking, parking violations, littering, or playing loud music in contravention of my local park's bye-laws.
You'll likely be able to successfully plead s3(1) if you used force against someone who was in the process of committing, say, a robbery or another violent crime, and you have a decent chance of deploying it if you used force to stop someone who was just in the process of pick-pocketing. It's not a license for members of the public (everyone who is not a constable) to use force when they witness what they believe to be a minor crime (such as a bye-laws violation).
Civilian detention powers ("citizen's arrest") under PACE apply to indictable offenses. Please don't try to do citizen's arrests on someone for a bye-law violation; false imprisonment claims can be fairly expensive for your employer.
Section 5(2) RoRA requires a request to actually give a name and address, which does not appear to have been made here (there are no implicit requests).
There's a reason detention powers for non-Constables tend to be quite tightly circumscribed. You run into Article 5 ECHR issues much too quickly otherwise. Which is also a reason why most TOCs AFAIK tell their staff to not exercise their s5(2) powers.