Ah, the sneaky little “Flickr.com” link at the bottom of the page. Not that obvious that that takes you to the full site. Thanks!
Also, for anyone else who cares, as is always the case, after trying to figure it out for weeks, I finally find another way 5 mins after posting the question in a forum!
Basically Opera Mini is your friend, as it gives you the option to “open an image”, which takes you to the raw image URL that you can then copy.
Thanks again for the most obvious method that I couldn’t figure out!!