Get webform submissions filtered by data value
The $filters parameter on webform_get_submissions() can be used for field filtering. The function's code loops over the filters and adds them as conditions.

foreach ($filters as $column =&gt; $value) {
  $pager_query-&gt;condition($column, $value);
}


So something like:

$old_form_submission = webform_get_submissions(array('email_field_name'=&gt; $provided_email));