A warm welcome to the forums - I am sad to see that no one picked this up, possible as your problem seems to point to a failure with btinternet.com ... which no staff member is likely to comment on, BT being Plusnet's big bad brother!
Would it be fair to presume that your email configuration for your BT email box is configured to use the BT SMTP server for outbound emails (not relay.plus.net)?
If the answer is yes, then this is entirely and issue with BT's email services - for some reason it has your IP address black listed.
As an aside to this, a problem seen recently having a similar profile identified that the user's connection to their PLUSNET mailbox was not using access authorisation (user name and password) for the outgoing (SMTP) server link. In some circumstances that can be detrimental to the submission agent's IP reputation. I'm wondering if this applies here?