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OK, my final report is... I eventually clicked the 'approve' link in the BT email. This simply presented me with a 'Thanks, your decision has been noted' message. A day later I got an email from my TLD host (TuCows) saying they had received an authorised domain transfer request from BT.
The email gave me an final opportunity to login at TuCows and decline the transfer if I wished, or alternatively do nothing if I wanted to allow the transfer to proceed. I did nothing and - as stated - the transfer took place a few days later.
The transfer-in fee and domain renewal was paid for by the BT account holder. There was no cost to me because 123-Reg/TuCows do not (currently at least) make a transfer-away charge.
Anyway, thx for the responses to my post. Also, to give credit where due, 123-Reg were prompt and helpful answering my support ticket about this.
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