Regardless of opinions about the police; I would send a letter with the cheque for £60, copied to my MP saying something like:
Dear Sirs
I am enclosing a cheque for £60.00 in relation to the fine issued by PCx and PCx on x date.
I would like to point out that I immediately undid my seatbelt as soon as I was pulled over as a matter of courtesy to the two policemen who I did not expect to have to come to my car to speak to me. I also thought it was helpful to get out and speak to them directly and face to face.
Whilst I appreciate the two officers may have been mistaken and quite understand this, I would like to point out that I was wearing a black top, sitting in a black seat and the seat belt is also black. In those circumstances I appreciate the two officers may have been mistaken.
I think it is a little regrettable that a fine has been issued in the circumstances and can assure you that I was wearing a seatbelt. I would find it most helpful if either of the two officers would provide any evidence that I was not wearing a seat belt and would be grateful to receive any photographs taken of me in the care that evidence that I was not wearing a seatbelt.
with best wishes.
Yours faithfully
The OP's BF.
If he really wasn't wearing a seat belt and is happy to send such a letter, I bet you get your cheque sent back.
And next time your bf is pulled over, tell him to stay in the car seat and pull down his window to speak to the officers; at which point he should ask if they would like him to get out.