Very many thanks for your responses thus far. Via TeamViewer, I have access to both ends of this email problem, and can update as follows on your latest investigation suggestions:
1)
the bigpond.com recipient's spam folder is empty of any TalkTalk.net emails. I've checked using both the bigpond.com webmail portal and also the Microsoft Outlook for Office 365 email client.
Further, the specific TalkTalk.net email address is shown in bigpond.com's contacts (both within the web portal and the Microsoft Outlook for Office 365 email client) and so unlikely to trigger a spam rejection, you would hope.
2)
I have sent two Plain Text format messages from TalkTalk.net to bigpond.com. One sent from TalkTalk webmail, the other from Microsoft Outlook for Office 365 email client (in both cases, accessing the UK-based laptop via TeamViewer).
Neither Plain Text message has reached bigpond.com.
3) Via TeamViewer, I have used the UK-based laptop (which is on the TalkTalk network) to login to a Gmail account, and send an email using TalkTalk network/GMail to bigpond.com. It arrived normally (and instantly).
By way of background, Telstra's Bigpond email product would fall into the legacy category, and is no longer being offered to new Telstra broadband internet customers (it was previously a freebie). I doubt this legacy webmail product gets much attention from Telstra's IT Support. There's a large old and grey user base (of which I'm one) currently prepared to pay Telstra's higher internet prices, because moving away from bigpond email is a hassle. This problem may be the trigger required for me to make the change.
Very much appreciate your assistance.
Edit 27/2 5:45pm Australian time
Happy to report that the issue now appears to be resolved.
I spent three hours yesterday with the Telstra Silver Member Support, during which we performed a number of tests together, all of which conclusively demonstrated that there is indeed an issue with this email traffic to Bigpond emails.
After three hours, the case was escalated to their dedicated Network team.
I have not yet heard back from that team, but this afternoon my time, email traffic appears to be running as it should, based on three test emails that I have sent from my TalkTalk account to Bigpond in Australia.
I suspect that something has been reset at the Telstra end, prompted by my support request. I certainly haven't changed anything on either the sender's or recipient's end. If I were to guess, I would put the blame on over-aggressive spam filters within Telstra, but that's just speculation.
