Happily I can write my final update on my case. Last Thursday TNT collected my old iMac, after having some issue as TNT could not find the information of my collection with the reference number they left me in a voicemail, and a TNT employee that could not find my address. After sending proof of collection to Apple I was told that the courier would contact me to set up a date/time for collection. I was afraid that it would take 6 days (as TNT was painstakingly slow) with booking an appointment, however that same night I was woken by a text message from UPS that they would deliver the item next day. And indeed, the next morning around 11 am the doorbell rang (ridiculously fast btw!) and currently I am typing this message on my brand new iMac.
Thanks all for helping me with this case and steering me in the right direction! I am happy that Apple, as a large company, did the right thing and made up for the mistakes made. For anybody in a similar situation and AppleCare is unable to rectify their mistake, definitely follow the tip of Antman and Aspekt, and find help from the boss himself! Even though, it is a large company, that does not mean that should be able to do whatever they want!
Now, back to my dissertation!

Thanks all for helping me with this case and steering me in the right direction! I am happy that Apple, as a large company, did the right thing and made up for the mistakes made. For anybody in a similar situation and AppleCare is unable to rectify their mistake, definitely follow the tip of Antman and Aspekt, and find help from the boss himself! Even though, it is a large company, that does not mean that should be able to do whatever they want!
Now, back to my dissertation!