Hi Ian,
you can always check start and end time of latest Inventory scan on appropriate managed client, switching "Task Runs" option in default "Collect Full Inventory" scan policy
Here is a Query according to profiler, when you refresh this place to see all clients and their start/end time of completed inventory scan
EXECUTE tmSelectTaskInstanceData @ParentTaskInstanceGuid='225067fa-37b3-4b3a-af01-a9c37bb553d6', @TaskItemGuid=NULL, @TaskInstanceGuid=NULL, @JobNodeGuid=NULL, @InstanceStatus=NULL
@ParentTaskInstanceGuid='225067fa-37b3-4b3a-af01-a9c37bb553d6' <--- This is a GUID of "Collect Full Inventory" policy, so you can specify there another inventory scan GUID to see required information.
Thanks,
IP.