If I had a hidden field which is only set by PowerApps, could I prevent everybody else from Updating

Nigel...

Hidden fields are hidden on forms only.  They will still be available for views.  What I was suggesting is a couple things:

1. Create a new form, including the hidden field, that is only accessible to the administrators.  You'll have to create a URL for them to access the form and then you can secure that URL (IE Page) to only those administrators.
2. If you need a view, create a new web part page and add the list/library to the page where the view contains the hidden field.  Secure the page to only administrators.  You'll also need to make sure that users cannot create views (personal or public), which would expose the hidden field (security settings).  To be clear, views are not secure able but pages with controlled views can be.
3. On the same page as the list/library, add another web part to include the same list/library with a view that contains the hidden field.  Use audience targeting so the administrators can see the hidden field in the view.

Hopefully this gives you a couple options depending on you're scenario.