Having the same issue on my iPad Air using safari. Before the update the reader worked fine. The updated site doesn't load any images or chapters. I have to switch settings to read off the legacy reader for me to load images
V3 of this site uses DOM storage. If you disabled DOM storage (which you should from a security/privacy perspective) and/or don't allow cookies for this website the site breaks.
Since you already have an account your problem is DOM storage not basic cookie decline. So the easiest way to fix it would be to enable the legacy reader (which does not use DOM storage) in your account options.