I think you may find that the UK CAA medical department will no longer advise you directly and will suggest you talk to an AME. This is a change of policy over the last few years.
They have however put a huge amount of their aeromedical guidance in the public domain. So if you go to
Centrally Acting Medication | Medical | Personal Licences and Training, then halfway down the page you will find an answer.The problem is that it probably is not the answer you wish to see. It states.. Gabapentin, pregabalin and carbamazepine prescribed for neuropathic pain and valproate for migraine prophylaxis are disqualifying for EASA medical certification because of the risk of unacceptable side effects.