On the face of it, this looks like a Linux hostname issue, and I spent a while setting up the ssh access to the box and searching for the hostname or server name - what I found turned out to the be private hostname / ip address, and therefore wasn't causing the issue.
I suddenly had a brain wave that maybe it was stored in the DB.
I then found I could login to the DB using the 'mysql --user=username --password=password' command. This allowed me to login.
I then found the schema for wordpress; https://codex.wordpress.org/images/9/97/WP3.8-ERD.png
Which I made a guess that it was the wp_options table.
I then did select * from wp_options, and put the result in a text editor and searched for the old domain name, and there it was under the option_name 'home' and 'siteurl'.
So I then used the following two command to update those values;
mysql> select * from wp_options where option_name = 'siteurl';
+-----------+-------------+-----------------------+-----------+
| option_id | option_name | option_value | autoload |
+-----------+-------------+-----------------------+-----------+
| 1 | siteurl | ***URL** | yes |
+-----------+-------------+-----------------------+-----------+
update wp_options set option_value='http://newdomainame/wordpress' where option_name='home'
update wp_options set option_value='http://newdomainname/wordpress' where option_name='siteurl'
And ran a commit for luck, and it all started working again.
