Articles 15 and 17 (dealing with deletion and access) both contain a provision where if the request is unfounded or excessive, you may charge a reasonable fee. You cannot charge a fee for compliance with standard requests, and "reasonable" is something that would likely be argued in court.

Source: https://ico.org.uk/for-organisations/guide-to-the-general-da...

Edit: mis-referenced article 15 as export instead of access.