Where does it say the tech log wasn't filled in ?
The AAIB report doesn't refer. However it does say, amoungst other things:-
No current pilot, engine or airframe logbooks were
found in the UK, preventing confirmation of the flight hours accrued. The total hours counter on the instrument panel did not match the recorded hours supplied by the Hungarian operator.
So without wanting to be smug I'd say if they weren't found in the UK either they were in a secret place OR they weren't filled in.
The AAIB report also says in relation to maintenance that:-
Maintenance work had been completed to change components without the knowledge of the approved maintenance organisation responsible for the aircraft. No record was found of who carried out this work or whether they had the appropriate training and approvals
Fluid levels within various components on the helicopter were found to be much lower than expected, with no obvious
leaks identified. This might indicate poor maintenance practices or missed maintenance checks