The additional email address was the only one to have been transferred to the new platform. They must be doing them one address at a time, rather than all those on one account.
To get it working again, I had to go to sky.com/tools and enable 'POP Download' for that address.
In Outlook Express, for that address only, change several settings, including some which are not normally altered such as ports.
You have been forewarned.