Here's my write up on how I've fixed it:
First thing I tired was contacting BT. My first call was not great, eventually I got through to a team who I was told would be happy to talk to me about the issues but they would want a credit card number..... I made my excuses and left.... ;-)
I tried again and got through to a grumpy lady who (after I asked if she could disable IP6 on the Home Hub 6) literally said:
and said I should send the Home Hub 6 back < sigh >
I went digging into the Home Hub 6 and found that I have both IP6 and IP4 public IP addresses, meaning things like my Tado which don't support IP6 can continue to work:
However my work laptop has an IP4 and IP6 address:
But doing so would break Direct Access on my laptop, which would be a Bad Thing (TM)
Instead I forced the laptop to prefer IP4 over IP6 by making the following registry change:
(reg change file here: https://1drv.ms/u/s!Arx7Ss1l4DQIgZSrJsx7M0EtARKBXuI)
After a reboot I'm in business!
Hope that this helps someone out there.