Can an appeal be made on the basis that a session was paid for but on the wrong vehicle and the records could probably show that said vehicle didnt enter the car park on said date?
Yes, however they're unlikely to completely cancel the charge. The BPA's Code of Practice (there's a link to it in my signature below) covers this situation - it's what's referred to as a 'keying error', where an error is made entering the vehicle reg when paying for/validating a parking session. There are 'minor errors' (one wrong character etc.), which should see the charge cancelled, and major errors (wrong VRM entirely etc.), that should see a charge of £20 levied.
From what you've presented so far, there doesn't seem to be much that would support an appeal other than the incorrect reg. With that in mind, if you appeal on the basis of the wrong VRM being entered, and making reference to section 17 of the BPA's Code of Practice, they should offer you the option of paying £20.