I was stopped by the Police who have accused me of using a mobile phone whilst driving. However I was not using the phone, I simply picked the phone up and moved it. It is therefore my word against the Police Officer’s. However, if I can produce a bill to prove that I was not using the phone, will the case against me be dropped?

You do not have to be speaking on the phone to be convicted. “Using” the phone can be as simple as moving it or holding it. The Police do not have to prove that a call was being made. Although it is for the Officer to satisfy the Court that you contradicted the regulations, just because it is your word against his does not mean that the Court will find in your favour. At the very minimum, you will need to put reasonable doubt in the mind of the Justices in order to dismiss the case.