The ICO says that the fee must be based on the administrative cost of providing the information which seems consistent.
Since you're allowed to respond to the first request with a list of the types of information you control, you should be able to do this without a search (and without undue costs).
"1 - The controller shall provide a copy of the personal data undergoing processing. 2- For any further copies requested by the data subject, the controller may charge a reasonable fee based on administrative costs."
https://gdpr-info.eu/art-15-gdpr/