[QUOTE=Genghis the Engineer;10685831]HB has, I think, pretty much nailed it, with the exception that your issue is the lack of a valid CofA. The Article 33 permission is clearly where you sit, but there will doubtless be a requirement to satisfy CAA that the flight is fundamentally safe.
That is correct if the C of A is temporarily invalid due to say non compliance with a maintenance requirement then the CAA will require to see the documentation that has been issued by the State of Registry that attests that it is safe to carry out the flight. In the case of a US registered aircraft that would normally be a Special Flight Authorisation issued by the FAA as per FAA Order 8130.2J Chapter 18.
Alaskaman makes reference to his company holding a "continuous authorisation" via Ops Spec DO 84 to authorise such temporary flights. I do not know what document and release of the aircraft is required under an Ops Spec DO 84 authorisation and I am not sure whether this would be acceptable to the CAA but it is well worthwhile asking CAA policy the question.