The hard fact is that, assuming you did not cross a line, this is cock up rather than conspiracy. If you intend to go to court and defend it you should do so from POV of disproving the allegation. This will mean revisiting the site, from both your perspective and that of the police car, and trying to understand why, if you did not cross a solid line, it might look as though you did.

Can you link to a streetview of area so we have a better idea of circumstances.

If/when you're acquitted then, should the circumstances sustain such action you make a complaint to the Police.

Going in front of a magistrate (or sheriff as you're presumably in Scotland) and accusing the Police of lying has a very high probability of ending messily.

The problem all of this is that it is the OP's word (and perhaps of his passenger) against a Police officer's. The OP obviously has no dashcam evidence, so the only course of action is to ask the Police (in court) to show video or photographic evidence of them commiting the offence and showing the road has either a solid line on the OP's side or a double solid line, or that the photo/video evidence whows them overtaking in an unsafe manner. I also agree with those saying that Street View would at least show if there are any solid white lines in the area in question, and the type of road being driven on (whether it was safe to overtake even if there wasn't any solid white lines down the centre).

In a he said-she said (even with the passenger [who can't be classed as an independent, unbiased witness] siding with the OP) case, the court will almost inevitably side with the Police, assuming for a conviction no photo/video evidence is needed.

I agree that the OP's belligerent attitude after being pulled over does not help, and won't be looked upon favourably by any court - they need to tell the truth in a calm, measured and above all, polite and respectful way. If they truly believe they have committed no (driving) offence, then they should consult a solicitor, who can advise them further. Might also be worth them going to the Law Forum website for some advice.

Saying all the above, I have my doubts as to the veracity of the OP's claims. Just a personal opinion based on the way they have put forward their version of events and reading similar posts from other people over the years on this forum.

Two points:

1. You need to consider what benefit it would bring to the police to lie. They gain nothing from stopping you or by sending a report.So lying is pretty unlikely - indeed if they lie and are found out, they will face disciplinary charges.

2. You might be better served at the roadside or in court if you go down the line of the officers being mistaken.

Without further information (Google Street View would be a start) no-one can comment very usefully on your assertions. It's a bit of a concern that you haven't told us the location.