The ACLS site generates a cookie using the last 2 parts of its domain:
Once this is proxied though it can often become something like:
The last 2 parts will then be ac.uk and the website will assume this is the domain and try to write a cookie to it which most browsers will not allow.
The end result is that proxying by any means appears to be only possible if the last 2 parts of your proxy hostname are longer than a certain length - i.e. using a single word top level domain such as .edu or .com.
If you are considering getting an additional domain and or changing your proxy server to gain access to ACLS, the OpenAthens service desk will be happy to test it for you.