What BT Hub are you using? Can get access to the Web GUI of this and login OK? If so can you check the Event log to see if there's any messages that look firewall related? You can access this via http://192.168.1.254 then on a Hub 5 it's Troubleshooting -> Event log, and on the Hub 6 it's Advanced settings -> Technical log -> Event log.
I never like doing this, but as a quick test it might also be worth disabling the firewall to see if this helps? On the Hub 5 and 6 you can get to this via Advanced settings -> Firewall -> Configuration and set the radio button to "Disabled". You'll need to click Save or Apply after you make the change.
This may help?
Windows sometimes has a habit of storing faulty parameters in its Registry.
Make sure you have any ethernet drivers at hand that you may need, then "unistall the ethernet device" and immediately reboot the PC.
The Ethernet device should reinstall itself.
If it does not reinstall manually.
Check if this has solved your connection problem?
I'll go out on a limb here and suggest the 'Smart Hub' has probably expired. There are numerous forum posts of problems with the thing. The sensible solution is to invest in a proper VDSL capable modem/router. If you complain to BT the best result you can hope for is they send you another Hub. A new one might work but for how long?
As confirmed by the tests you carried out it seems your connection is working fine and the problem is confined to the hub.
If this is happening on different devices and you have already had a replacement Smarthub which made no difference it sounds more like this is a network problem and not a problem with your equipment.
Try switching off your Smarthub for a couple of hours to see if it gets issued a new IP address and if that doesn't help post back to see if the moderators can help.