No, as suggested by Vodafone, I am using the same simcard, and carrying out a Restore via iTunes: "The iPhone has now been unlocked – Please replace the SIM (use a SIM which has never been used with this iPhone) and connect to iTunes or perform a software restore via iTunes."
Process: when I had received the message saying that the iPhone was now unlocked, I connected it to this MacBook Air, and used iTunes to Restore. Everything seemed to proceed normally, with the progress-gauge showing that to be the case, but finally iTunes said that it could not verify the device.