TC will not find my wireless network

(1) could it be that the reception ability of wireless signal on the TC is faulty? Is there a way of checking? (I have rebooted once already)

Possible, but highly unlikely.

(2) is there a setting on the BT Hub that enables extension (Unlikely as the AirPort Express works)

No. If you have an AirPort Express that is wirelessly connecting to the BT network, it is "joining" that network for use with AirPlay or a remote USB printer. The Express cannot "extend" the BT wireless network signal.

To confirm, here is what Apple's product information sheet says about the AirPort Express:

Extend an existing Wi‑Fi network’s range.

If you already have a wireless network in your home and want to extend its range, AirPort Express can help. Just place it in range of your primary base station — an AirPort Extreme, AirPort Time Capsule, or another AirPort Express

Like the AirPort Express, the TC can only wirelessly extend a network that it being provided by another Apple AirPort router.

If you can connect the TC to your BT hub using a permanent, wired Ethernet cable connection, then you can configure the TC to provide a wireless network signal.....which the AirPort Express can wirelessly extend (assuming that you have a recent version of the AirPort Express).

does this mean that the TC will not receive unless it is from an Apple product?

Yes, that is what I meant when I said that........the TC can only wirelessly extend a network that it being provided by another Apple AirPort router.

I am sure I have read it will receive from any router if set in Bridge mode (mine is)

Unfortunately, if you did read that the TC will wirelessly connect to a third party wireless network, what you read is not correct.

Your second statement: The whole reason I acquired the TC was to have it running an extended network some distance from the router (and provide networked printer access)

Then, if you are not willing to connect the TC to your BT hub using a permanent, wired Ethernet cable connection, you may need to return the TC for credit or a refund.

Even if the TC could do what you want, (it cannot), this would be the worst possible way to connect the TC to a network.....since you would have a "double hop" wireless situation if you did this.

I'll see if I can get a refund... can't go till next week

It might be a good idea to check with the store about their return policies. In the U.S., Apple will allow 14 days to return a product for credit or a refund.