Q. Do we subscribe to a database of questionnaires?

We subscribe to Health and Psychosocial Instruments where you can search for questionnaires: http://www2.le.ac.uk/library/find/databases/h/healthandpsychosocialinstrumentsdatabase

[choose Health and Psychosocial Instruments when you login]. As its name suggests it is focused on health and psychological research. Most of the results will be for publications that contain questionnaires within them. It does not provide 'off the shelf' survey forms. 

UK Data Archive has a Variable and Question Bank. This allows you to search for questions that have been asked in the surveys held by the Archive https://discover.ukdataservice.ac.uk/variables