From what you say, it appears you have already been to Court & been found guilty. If the facts are as you have set out, this looks very like a miscarriage of justice - assuming the facts were properly explained to the Court & any necessary proof was given.
You need urgently to seek legal advice with a view to appealing. You can go to the Independent Police Complaints Commission (see website) to make a formal complaint about the police force involved & you should probably do that as well as appealing, but talk to your solicitor first.