Try using:
$booking = new WA_MySQLi_RS("booking",$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 ? AND carpark.name LIKE ? AND Tel LIKE ? ORDER BY Date DESC");
$booking->bindParam("c", "".$_GET['S_Email'] ."", "-1"); //colname1
$booking->bindParam("c", "".$_GET['S_Name'] ."", "-1"); //colname2
$booking->bindParam("c", "".$_GET['S_Tel'] ."", "-1"); //colname3
$booking->execute();
Using "c" as the data type should automatically add the '%' at both ends.