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In the letter you received, it tells you to ring the 0800 number. When you do, they order the SIM for you, and also give you the PAC code to allow BT to move you from the BT Mobile (Vodaphone) to BT Mobile (EE).
Be aware, if you use Broadband Talk, you will lose it if they move you onto a different broadband package.
The lady I spoke to on the phone was very helpful. Asked me if I was on BBA, and wanted my number ported. She asked for my number, went away for a short while, then came back on the phone with my PAC number.
I entered the info into the webpage, and my number was ported two days later.