Bakery with Varnish over HTTPS with Nginx [#2744123]

I'm working on a site that uses Bakery 7.x-2.x-dev for SSO.
The Bakery SSO works fine, but we are looking to put the site behind Varnish.
The Bakery master is actually a Drupal 6 site, and the slaves are Drupal 7.
We have a staging site that works against the same master site as the live site, and Bakery works fine without Varnish.

On the staging site we have now added NGINX to terminate SSL and Varnish to cache pages in front of Apache which serves Drupal.

We've added the specific cookies to the Varnish VCL to ensure they don't get stripped.

However, with NGINX and Varnish enabled, when a user attempts to log into the slave site, we are bounced back to /bakery/login and the browser reports a redirect loop.

Can anyone suggest why this might be and how to resolve?

There is nothing in the watchdog other than repeated "Session opened for test-user" entries.