I haven't done it, personally. But I believe they (like many embassies) are exceedingly picky about the process.
I believe that you can appeal... but it's much better to give them exactly what they ask for, and endeavour to do everything you can to ensure that they say yes, first time! :-)
I would therefore encourage you to follow EXACTLY their instructions, and make sure you provide all the documents they specify.
If you already had an interview you are very far along, nearly there! If you have a date for your appointment, then that's pretty good. If you haven't emailed them yet, then you have a lot of work to do. :-)
Most of it is fairly straightforward, but you do need a medical certificate (which might be slower to obtain because of Covid and NHS backlogs), and a legalized ACRO (also takes a bit of time & money), and the Spanish health insurance might be a bit of a pain to sort out remotely (and might cost 500-1000 euros on its own).
Their list of all requirements for the VISADO DE RESIDENCIA NO LUCRATIVAÂ is in the following official document:
and VISADO DE RESIDENCIA Y TRABAJO POR CUENTA PROPIA here:
The following will illustrate how specific they are about their application process:
"Applicants must request their appointment through the following procedure:
1.- Send an e-mail to the address cog.londres.viscp@maec.es.
  In the SUBJECT you must specify the type of residence visa you wish to apply for.
  The TEXT of the message must state:
    - GIVEN NAME AND SURNAME
    - PASSPORT NUMBER
    - E-MAIL
    - PLACE OF RESIDENCE IN UK
    - TYPE OF RESIDENCE VISA YOU WISH TO APPLY FOR.
  Each appointment is only for one person, therefore, family members accompanying the applicant who wish to apply for a visa need to book an additional appointment.
2.- Attach to your e-mail one essential document:
d) Investors, Entrepreneurs and Non-lucrative residence visas: Sworn translation into Spanish of ACRO Criminal Record.
e) Self-Employment work visa: EX-07 form filled.
  Failure to attach this essential document to your e-mail, your request of appointment won’t be processed.
  Once your document had been verified by our staff, you will receive an e-mail with a username and password to complete the process.
  Applicants are strongly advised not to send more than one e-mail requesting an appointment, any reiteration will lead to a delay in the processing of their visas.
3.- Once you receive the confirmation e-mail with your password you could choose the date and time of your appointment, and modify or cancel if needed."