Where can I find the full list of parameters available in the API? Is there any documentation around this?
The general documentation is here:
https://developer.company-information.service.gov.uk/
The official API documentation (for the “main” API - public Dat API - and others) is here:
https://developer-specs.company-information.service.gov.uk/
The collection of values (and text to go with them) returned by the API is here:
There is an unofficial guide to some of the APIs here:
https://chguide.co.uk/
What parameters in particular are you asking about?