You can certainly continue to use Thunderbird, that is just an email client. However, the rest of your post implies you are using webmail, rather than POP3/IMAP and SMTP. That confuses me, as the whole point of Thunderbird is that you don't use webmail for the bulk of your emailing, and your Address book would be on your computer.
Do the emails get downloaded to your computer? Is your current Yahoo email address set up in Tools >> Acccount Settings in Thunderbird with POP3/IMAP and SMTP?
Unfortunately the link you give to the BT help doesn't work for me, so I can't read the rest of it to see if that tells me more about the problem.
It is probable that BT mean they are blocking port 25 for other SMTP (email send) services than their own.
If this is the case there are two solutions.
The better of the two may not be provided by Yahoo, but most decent email hosts have their SMTP server listening on more than one port. You should be able to find if Yahoo do this through their Help or FAQ systems. Look for Port 25 blocking and SMTP setup, that sort of thing.
If they do an alternative port then BT may not be blocking that. The BT Help should be telling you exactly what ports are blocked, perhaps in that link that doesn't work for me. You set the alternative port in Thunderbird >> Tools >> Account settings >> Bottom of left-hand menu "Outgoing server (SMTP)".
The other way is to use the BT SMTP server for sending, as they say you must, which you set in Thunderbird at the same place as the alternative port, but you simply make sure in the main "Account Settings" page in Thunderbird you have your Email Address and Reply-to Address set to your existing Yahoo address, leaving the POP3/IMAP settings unchanged.
Does that help, or have I misunderstood?
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Edited by RobertoS (Wed 04-May-11 09:21:03)