I'm having same issue with btinternet.com domain, but on larger scale. I work in publishing and we have 28k of users from this domain that we can't email, as the emails are being returned (bounced).
The issue started in April and is ongoing, many of these users are paying for subscriptions, which we can't honour, as we have had to stop sending to them. The issue started in April and I assume must be related to software updates at BT, postmaster feedback indicates that issues with Links have resulted in our IP being added to invalument register (blacklist). To put in context we 12m emails per month across 1000 campaigns. We have no issues with any other domain or ESP, just BT. Our bounce rate from btinternet.com is 100%, the rate for the next highest domain is 0.5% - something definately amiss here!
So far I have yet to see this explained.
The OP said that it has just started to happen, meaning it was fine up until then. So what has changed ?
Suerly every business that send bulk emails (obviously to include btinternet addresses) can't contact the postmaster to enable them to be logged or whatever it means. That could be 10s of 1000s of businesses globally.
Do you really expect them all to do that?
What will happen is that btinternet email address users will find themselves more and more cut off, possibly causing serious issues.
This is not a simple matter of contacting the postmaster, it is something else that needs fixing.
You will also note that he has already probably contacted the postmaster, unless it was an auto-response. Links in emails should NOT trigger blocks, typically businesses have a link (to effectively abide by the law) to enable end users to opt out of mailings.