What "logbook" is missing?
Normally, on a G, you have the airframe logbook and the engine logbook and, if the prop is VP, a prop logbook.
The only way to reconstruct those will be from individual pilot flying records. The CAA will have only the hours at each Annual on file.
I would start at the maintenance company/ies and then get the pilot logbooks for flight data. The maint company will have the total times for the three items at the last Annual.