WP wp-admin/customize.php invalidates session

Question

I moved a wordpress installation from one server to another server and the newly moved installation got a new URL as well - move was done to get a test environment.

Now when I access wp-admin/customize.php?theme=Name-of-my-theme the session expires and the log on box shows up.

I can return to the wp-admin and navigate the admin area without any issues. If I just pick wp-admin/customize.php from the navigation in the wp-admin area I get the same issue - session has expired and I have to log in again.

When I then try to log in through the log in box on wp-admin/customize.php it's not working, the page reloads and asks me to log in again.

Name of the design theme is U-design.