Ok I can see that others have been having issues with BT for over a week now https://downtoday.co.uk/bt-email/
This really seems like they are having issues on their end which is likely what is causing you not being able to send into their network. Probably the best thing to do for the time being is to send to your BT users only from your BT account until this is sorted.
The issue cannot be fixed from your end since it is their problem. Aside from using your BT account you can email the BT postmaster directly and see why your messages are not getting through. Send an email to email@example.com
They will be able to see if your mail server was blacklisted or if this is just a problem on their end for sure. But from what I have found it looks like an issue on their end that they are working on.
Email issues like this cannot ever be corrected on the senders side unless you were blacklisted which means you need to email the postmaster to get off the blacklist. But based on what you have told me it does not sound like you have done anything to warrant blacklisting, usually you get blacklisted for sending many emails (spam) into BT's network and does not sound like you did that.
So unfortunately all you can do at this time is use your BT address to send to BT people and let BT sort it out. If you want to be sure it is an outage send an email to the postmaster address I gave you just to be sure however I would not expect a quick reply. Also if you are a current paying BT subscriber you can contact them here:
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