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Plugin for Contact Form 7: adds a field for an unique submission id.
You can choose to include a hidden or an visible field to your form.
This field will be automatically filled with an number which is incremented on every submission.
Just add the field to your form.
You can filter the value using the cf7_submission_id_filter.
To add leading zeros for example, just put the code below in your functions.php
add_filter('cf7_submission_id_filter', 'custom_cf7_submission_id_filter');
function custom_cf7_submission_id_filter($val){
return sprintf("%04d", $val);
}