There seems to be no specific "appeal" procedure in case a grant under the scheme is refused.
This is (was) a government scheme, which is (was) run through the local councils.
These are grants, not loans, provided by the government, not by banks.
I can't think of an involvement of the Financial Ombudsman Service, also given that the funds are granted based on eligibility criteria that are objective and can be verified.
However, in allocating the grants, the local councils have to be impartial and they cannot consider as eligible a business that is not nor consider not eligible a business that is eligible instead.
Based on what you say, I don't think your business was eligible, but, if you think it was, you can obviously complain to the council.
The council is obligated, if you ask, to provide you with their complaint policy - which they must have for governance needs - and, at any rate, you may complain by email using the contact for enquiries.
If there is any wrongdoing by the council, you might also considering bringing them to court, but - even more because you don't seem to have a case - you should consult a solicitor for an assessment of the case.
As you know, the scheme is now closed, therefore this could be a practical issue anyway.
I hope this information is helpful and I wish you the best.
Please do not hesitate to contact JA again if you need help and you may ask to speak with me directly if you wish.