The GP practice may or may not have the power to cancel the invoice, depends on whether it is them that contracted the PPC and what is in the contract regards cancellations.
As for legal recourse, nothing you can do at the moment, the ball is in their court. You will now get lots of letters from a debt collection agency probably followed by a letter of claim which may or may not end up in a court case. If it gets that far come back for more advice as "I'm a regular customer but forgot to register despite knowing the rules" isn't a great defence.
Bottom line is you failed to follow the terms for parking which gave them a reason to issue a PCN, your mistake has cost them money, sending out the PCN, follow up letters and dealing with your 2 appeals isn't free and they want their money. Your disabled badge status isn't relevant in this case unless you can show they haven't made reasonable adjustments to allow you to comply with the car park terms, e.g. the terminal is inaccessible to a wheelchair user.