Usually the CAA would need to see a robust Safety Case that proves a net increase in overall runway safety levels before granting approval for any plans that require a derogation of 'grandfather rights' to be continued. Maintaining that the runway is a proper Code 4c runway -for the sake of a few metres TODA length - is hardly a net increase in safety, when the runway width is so out of kilter with the requirement.
I would imagine it will have to revert to a Code 3c to gain CAA approval.