You could not allow null in that column and set the default to an empty string instead.
Another option is to complicate the SQL statement to account for it like:
$booking = new WA_MySQLi_RS("booking",$georgeconnect_i,0);
$booking->setQuery("SELECT carpark.*, contractcar.ContractID FROM carpark LEFT JOIN contractcar ON carpark.CarID=contractcar.ID WHERE Company='Ascars' AND (carpark.email LIKE ? OR (?='' AND carpark.email IS NULL)) ORDER BY Date DESC");
$booking->bindParam("c", "".$_GET['S_Email'] ."", "-1"); //colname1
$booking->bindParam("c", "".$_GET['S_Email'] ."", "-1"); //colname2
$booking->execute();