New commerce site checkout broken
Checkout problem - there are two possibilities that fixed it, as I re-enabled Extra Panes and Coupon UI at the same time.

I had set an extra field in Customer Shipping Profile. I didn't think it was dependent on Commerce Extra Panes, but when I disabled that module the process broke.

It could also be that the coupon UI module provides the text box on the checkout process, so when I disabled that it broke it.

Thanks for everyone's help in the comments above :)