Not sure if the old BT box or Samsung TV retain a DNS cache or not. Since it's all on a ethernet, then maybe it can all be cleared from my PC...or maybe not.
So are you using BT, or this other tinpot ISP (which sounds more like a pisspot VPN provider than an ISP, and I think I know who it is
). If you are using BT, then stick with the BT Hub, and FFS stop using VPNs!
The BT hub does some, but minimal caching. Restarting hub clears the cache, though it will soon clear itself. Worth checking if you are using the BT DNS servers, or if you have put something else in - beware that large ISPs can (and often have to by law) hijack the DNS anyway, so it probably won't be going to where you expect anyway.
The device (TV in this case) will have a DNS cache onboard as well. Clearing them can be a pain, because most are running some form of Linux. Probably turning it off at the wall is a 95% way of clearing it.
But it's all 'dangle berries' anyway, because streaming services use local content providers, and these all have a short TTL on the DNS, so realistically should not be in any cache. If it is DNS related, it's most likely to be due to VPNs being used through the router.
In short, stop using internet to internet VPNs. There isn't a good reason to do so, unless you are freetarding iPlayer, and we know that ain't worth the effort.