There are plans to remove the small company p & l exemption and new rules on verifying directors ids. Costs are going up too. It looks like a CIC you can only file online if full accounts. https://find-and-update.company-information.service.gov.uk/a...
You have to keep accounts if a business even if not incorporated. A company has to keep accounts if it has any assets (e.g. a domain) or any financial transactions (e.g. paying for hosting)
You will also probably have to file a tax return. You have to keep a register of shareholders.
It is relevant this case. The thread is about moving an activity that is not a business to a company (and for some reason a CIC in particular). If you did it in your own name you would not have to keep accounts.