If you are moving the site to a new URL the WordPress database will not be changing so all you want to do is to move the entire WP directory to the new folder on the same server or new server on the same hosting.

Simply edit the wp-config.php file:-

define('WP_HOME','https://www.chameleonwebservices.co.uk');

define('WP_SITEURL','https://www.chameleonwebservices.co.uk');

Note: When you do this the new server url will shown grayed out in the WordPress Admin backend and you can not edit it anymore.