What about amending your logbook to reflect the hours as P1 as stated above and then write to the CAA setting out formally the following:-
- state that you were the sole manipulator of the controls
- provide evidence of you having paid the flight school for P1 hours - presumably less than the dual rate. Give them extracts of web print outs etc and credit card statements. Reference these up properly and cross refer to them in your letter.
- hang the instructor out to dry by stating that he did nothing and should not have logged hours as it was not an instructional flight, he was just a passenger and a close acquaintence and it was incidental that he was an instructor.
- point out that you already had a PPL and so why would you fly with an instructor as it makes no logical sense whatsoever
- try and get a letter of support for your case if you can from the flight school (hard I imagine)
- state that you are willing to make a signed affidavit in front of a lawyer stating that the above is true and fair if the CAA require this
For the sake of a bit of time drafting a formal letter and a stamp I would go down this route. Remember to be polite but to the point in your letter. Quoting applicable references to the ANO might also help and make the CAA realise that you are not going to be fobbed off. Remember they have rules to follow as well and they can't decline you if you can prove you were correct.
Good luck.