Utilising Key Pairs for Authentication isn't currently supported under Cyber Essentials other than for secondary authentication.
Unfortunately, the use of key pairs for login authentication on its own as an authentication method is not supported under Cyber Essentials and therefore, you will have to utilise Usernames/Passwords, using key pairs for Secondary Authentication.
The current statement from IASME in regards to Key Use is: Though a secure method of authentication at present it is not recognised under Cyber Essentials and password-based authentication is the only method. However, it can be used as a second factor of authentication as this method means the device with the private key is a trusted device.