call_user_func_array
“Call a callback with an array of parameters”
call_user_func_array(array($stmt, "bind_param"), array_merge(array($type), $params));
should do the job
UPDATE: you have also to change your params array:
$params = array(&$firstName, &$lastName, &$address, &$postcode, &$email, &$password);
as mysqli_stmt::bind_param
expects the second and the following parameters by reference.
EDIT: Your query seems to be wrong. Maybe you have less fields than you have variables there. Do:
"INSERT INTO Users (field1, field2, field3, field4, field5, field6) VALUES (?, ?, ?, ?, ?, ?)"
where you replace the name of the fields by the correct names