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Had a few run ins with the met traffic and west mercia traffic. Most have which ended, after much hassle with letters of service falling below standard and some even got me a pay out, as the Met officers lied. Yes I am still bitter, having several witness of other drivers, a paramedic unit and being carted off in an ambulance all before the Police arrived and discovering I had failed to produce my documents. While the other driver, failed to stop after an injury collison, had not tax, insurance or MOT and the met police didn't prosecute him for anything but I got prosecuted for failing to produce documents.
Flipside is Warwickshire traffic officers can be quite nice.
Probably no in car video then, your word against two coppers. Let us not go there on that one.
So IMO your choice is take the fine and points. See if the points and poinsts code effect your insurance premium. Speeding doesn't but what the points you are being issued at a guess, due care and attention, may cause an increase in premium.
Or go to court, piss an overpaid right wing twat off (especially as it will be road offences) and the twat will not be paying attention to you or the pleadings as he (mostly) will be reading the notes to the next case, or wondering what time lunch is.