drupal_add_js does not support an ID attribute as it seems.
However, as a workaround, you can use drupal_add_html_head to add stuff to the head section.
$element = array(
'#tag' => 'script',
'#type' => 'html_tag',
'#attributes' => array(
'src' => 'https://www.docserver1.co.uk/dsxc/client.js?acc=xx&integrated=true',
'id' => 'dsxc_script',
//dpm(drupal_render($element)); Gives the following:
You can always embed these scripts in your html.tpl.php file, but if you want to add the stuff conditionally, I think this will work.