Shame.
I suggested the following while you were typing!
'We, the creditor, now request this amount is paid....and if you were not the driver...' which is a direct quote from the PCN would, IMO, be accepted as an invitation to the keeper to pay, after all the PCN's addressed to the keeper.
OP, IMO you should appeal to Premier Park and then to Tesco in that order.
You appeal to PP in such a way as to invite them to ridicule your claim to de minimis, even assuming one accepts a breach at all, and to not give due regard to the BB and your/your passenger's needs. You would also point out no-one was impeded or inconvenienced and that elsewhere in the car park, as indeed is common practice with all off-street car park providers and a regulatory requirement on-street, the designated bays for the disabled are wider than those for other cars for the obvious reason that in general they require more free space to enter/exit their vehicles. It could not have escaped the attendant's notice that a BB was displayed and therefore more room needed. You accept that it was not a designated bay, but cannot imagine that Tesco intend that BB holders should drive off without shopping simply because they cannot access a disabled bay for fear that an employee of their parking contractor believes that these drivers are fair game for £100 parking charge simply because they need a little extra space in a regular bay.
A BB holder's needs don't change simply because they cannot park in a disabled bay.
As thick as you like to make it.
AND THEN if they reject you go to Tesco with your appeal and appeal and say 'I tried the method you advise in your store and this is the considered response of your contractor. I would kindly ask that you exercise better judgement and instruct them to cancel'. But you're not there yet.
To do it vice-versa risks you missing the contractor's appeals deadline while you wait for a reply from Tesco and the contractor disregarding because you then submit an appeal late.
There will be other views, but do not wait too long and risk missing the PCN deadline.