I had a reply back from Apple Support. This is what they suggest, if it helps anyone else - I am doubtful the first steps described will help me but am off to try them now...
Thank you for contacting us.
I understand that you have been unable to access Podcasts Connect to submit your podcast as it continues to loop you to the login screen.
To troubleshoot this issue, make sure that your Mac is authorized in the iTunes application.
1. Open iTunes.
2. If you’re not signed in, sign in with your Apple ID.
3. From the menu bar at the top of your computer screen, choose Account > Authorizations > Authorize This Computer.
Next, download or purchase an app using your Apple ID (this can be a free item); this will ensure your Apple ID is fully enabled for the iTunes Store.
Last, please clear your web browser’s cache, cookies, and history. Once you have completed these steps, please try to access Podcasts Connect again. You can also try to submit your request from another web browser.
If you are still receiving this error, please provide the following:
• Steps to reproduce the issue
• Full-window screenshots or video illustrating the issue
• Username of each user experiencing the issue
• Web browser and version number
• System information (device model and OS version number)
• Approximate date and time the error occurred (including time zone)
• The URL of the page
• Source code of the error page
To obtain the source code, right-click the error page and select Show Page Source. Please copy and paste the source code (do not attach it as a file) in a reply to this email.
After we receive the requested information, we will investigate further and let you know when we have an update. Thank you for your assistance.