HTML Tags being removed if button isn't present

I customised the toolbar to remove the Image and Table buttons
The editor then stripped out any img or table tags in the HTML 
I added the buttons back to the toolbar and now it allows those tags,

But it's still stripping numerous other tags (<div>, <style>, etc) that were fine in an older version of CKEditor.

I can't find where to control this behaviour. I've found how to disallow certain tags, and there's nothing in the config.js file to disallow any tags at all. 

How do I make the editor NOT strip these HTML tags?

Thanks in advance for any help/pointers you can give,.