A little more information on this problem...
I have just tried updating another completely different site. This site was running Joomla 3.1.5 with Gantry 4.1.18. Prior to updating, I checked the template and everything was fine with Gantry's admin panel.
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I then updated Joomla to 3.2.1 and looked at the template's admin panel and noted it was now broken.
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After that, I updated Gantry to 4.1.20 and noted Gantry's admin panel was still broken.
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As I have said previously, I have deleted all site & browser caches. I have even tried reversing the order of the updates (Gantry > Joomla and Joomla > Gantry). Today I even tried updating using different PHP versions (5.3, 5.4 & 5.5) but the result is the same. I have tried updating on my localhost as well as on a live web server.
I did note that after updating Joomla to 3.2.1 and leaving Gantry at 4.1.18, although I could open the template admin panel, none of the buttons or controls functioned. However, after then updating Gantry to 4.1.20, the buttons and controls worked again although the layout of the toolbar remains broken.
I'm keen to get this resolved if anyone has any clues? I have a bunch of sites I was planning on upgrading but I'm reluctant to now that it appears to be some sort of conflict between Joomla and Gantry.