A completion certificate proves Building Regulations work was checked and approved; it's separate from planning permission.
Under the Building Act 1984, certain building work must be checked and signed off by Building Control.
Work on listed buildings usually needs listed building consent as well as Building Regulations approval.
Planning permission and Building Regulations approval are legally separate processes and both may be required.
Carrying out notifiable work without Building Control approval is an offence under the Building Act 1984.