Well lucky you. I've had exactly the same issue. Spent ages talking to what appeared to be a very helpful lady who said the accidently un-linked accunt would be available to re-link in 2-3 days but 6 days later still the same 'sorry...' message! This must surely be a BT system fault if it is happening to others so why can't they sort it. Problem all started for me when we found our POP3 option was turned off on 11 August by BT so all emails then came in source code. It was while trying to sort this that I accidently un-linked my wife's email address. Would consider switching to a different provider but too much hassle.
It wasn't luck that resolved this it was the OP contacting the BT Email that got the problem resolved. Perhaps if you do the same you might get a similar result.
@sam63 The link on the My BT page does not work. There is no other way to re-link the email address. You'll need to contact CS and ask them to do it.
Interesting, I have had a similar issue which has now been going on for 4 weeks, incidentally all started when BT terminated my POP3 emails and started sending everything in IMAP. In trying to resolve the problem I inadvertently deleted or unlinked my wwife's email account from my master account. I've spoken 3 times with BT technical support who all say 'we understand the problem and it will be put back into your account by BT within 3 days'. Well I'm still waiting and I really do not have the time for yet another 45-60 minute call to BT. I simply cannot understand why it hasn't been done by now.
BT did no such thing, the choice of IMAP or POP3 is made by the client configuration, not by the server.