It's not easy, especially when you consider that the workspace might be only partly synced to that label. i.e, the label was used with a more restrictive path than that in the label itself.
One rather crude method is to take each label that might apply to the workspace (you can determine this by the view in the labels, or if you use a meaningful naming convention) and do a test sync (p4 sync -n) of each one in the workspace. With luck, only one of them will show zero actions. However, it's possible that more than one will seem correct, or that none of them will.Essentially, you're trying to access label information backwards.
They are aliases for a particular state of the repository, but are not a state in and of themselves. (I.e., "synced to which label" isn't really meaningful in Perforce.)
If you need to duplicate the state of a workspace into another workspace, are you aware that workspace names are also labels?
You can sync one workspace to the same state as another by using the other workspace's name. (Assuming the views are compatible.)
The administrator has disabled public write access.