Presumably he had photograhed your reg
That gave him 14 days to get an s172 to the registered keeper, starting at least 33 days ago from the OP. If the bike is registered to you at your present address, so you could be sent the s172, and you haven't received it, then the alleged offender cannot be prosecuted unless it was sent registered post and not returned undelivered.
IF he'd stopped you, cautioned you and recorded your response in his pocket book, and your response wasn't a flat denial, then he'd have had have some worthwhile evidence to take to court should you refuse the conditional offer of a fixed penalty.
But he didn't, and had no evidence of the alleged offence, no other witness, no photo, no admission. I trust you weren't sent an s172?
P.S.
If stopped there are two ways to go about it. Act as a simple hapless victim, politely and apologetically admit whatever, hoping for leniency - it may work. Or, if it's a single officer's uncorroborated observation, no video, no VASCAR, etc, then act like you have a lawyer prompting you, "No officer, I'm very sorry, you must be mistaken, no part of my vehicle was across the solid white line at any stage / the traffic light was showing GREEN as I continued across the regulation line / etc". Under PACE your response must be taken down word for word, and is part of the evidence should the officer wish to act on their apparently inaccurate observation. A fixed penalty could be issued out of spite, but without tangible evidence the case will not hold up in court. This came from someone who had the other get out of jail free card that worked a few years back - a warrant card.
