Thanks, but it's definitely not a temporary problem.
It is ongoing, which is why I had to find a workaround and stumbled across the issue being with the HG612. I changed hardware
because of the problem.
The BT Smart Hub 2 does not have the problem.
The TP-Link W9970 does not have the problem.
I can plug either of the HG612 back in and the issue reappears. So I can reproduce it on demand.
And I can reproduce the traceroute, and accesses/timeouts to specific sites.
The gateway issue could be a reason, but only if plugging in the HG612 landed on the same problematic gateway every time. Which feels like a bit of a reach. That said, I'll keep track of their numbers.
ps: funny that the site says I've "just arrived" even though I've been a member for 10 years