This is from the Firearms Act:
Special provisions about firearm certificates.
[
F7(1)A firearm certificate shall be granted where the chief officer of police is satisfied—
(a)that the applicant is fit to be entrusted with a firearm to which section 1 of this Act applies and is not a person prohibited by this Act from possessing such a firearm;
(b)that he has a good reason for having in his possession, or for purchasing or acquiring, the firearm or ammunition in respect of which the application is made; and
(c)that in all the circumstances the applicant can be permitted to have the firearm or ammunition in his possession without danger to the public safety or to the peace.]
When an application is refused, the police write to the applicant giving reasons for the refusal.
If the applicant thinks those are not "good reasons" then he/she can can appeal
Also, bear in mind that we only have the OPs side of the story to go on - we are not privvy to all the information the police had when coming to their decision
Cheers
Bruce