When fulfilling requests, businesses will on occasion request further ID&V to make sure you are who you say you are, or double check the requested action, especially in the case of an erasure request as it may be a company that stores loyalty points for you for example!
Through the Protect service, your requests were sent from your personal email so for most businesses this should be proof enough.
Companies should not request more information if the requesters identity is obvious to them so an email from a registered email address should ordinarily fulfill this! Anything beyond this should be reasonable and proportionate to what they are likely to hold on you.
Eg. Sainsbury's shouldn't be requesting photo ID as they don't hold a copy however your bank will likely choose to do so and are within their rights to.