Are companies obliged to issue a certificate of hours if the worker so requests?

Yes, according to regulatory point ORO.FTL.245 (b):
‘On request, the operator shall provide copies of individual records of flight times, duty periods and rest periods:

1. the crew member concerned, and (
2. another operator, in respect of a crew member who is or becomes a crew member of the operator concerned.’

However, paragraph (a) of the same point provides that the mandatory period for the operator to keep individual records for each crew member is 24 months.