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Seems there is a general issue going on at the moment.
The DNS resolves to multitude of different IP addresses, and keeps changing and swapping IP's.
None of the IP addresses authenticate.
are you using web mail or outlook or a mail client?
just tried sending and receiving on my btinternet.com account and works ok
Mail clients, using SMTP / IMAP. Also doesn't work on the smartphones using a different data carrier.
just tried again using android and sending and receiving works no problem I am not a BT mobile customer
are you a BT broadband customer?
Have you recently setup 2 step authentication?
I recently set this up and a password change was involved.....I came unstuck with the iPad BT mail, where on my particular setting, the outgoing smtp required the password. This had changed and blocked outgoing mails.
Check your email settings.