It seems you cannot take any advice or help, if it differers from your view.
I have little doubt that charges for 1471 or 1571 are shown on the bill, they are for pressing 5 and trying to connect.
I believe that the message gives warning of a charge with the automatic redial (pressing 5) If you just hang up and dial as normal there is no charge.
'Tis the pressing 5 that cost and you will be happy to know that it is charged regardless of a connection. so if you get the engaged signal it is still 20p on the bill.