Thanks for the replies.
Logic would suggest that if, as a CPL holder, your medical certificate stipulates the date until which you can exercise Class 2 privileges then your licence would be valid were you to fly privately. However, the following statement suggests that a CPL holder must always have a Class 1 medical to fly:
"Part-MED stipulates that applicants for and holders of the CPL(A) shall hold a valid Class 1 medical certificate".
Does 'valid Class 1 medical certificate' mean that your Class 1 privileges must be valid or that you can have a Class 1 medical certificate which is validated by the Class 2 expiration date if the Class 1 privileges have already expired?