In case anyone else has the same problem in future, I discovered that the Home Hub has a mysterious "Wireless Mode" setting which I have never seen before. The options are not described on the page (only as Mode 1, 2 or 3), but I found this information online:
What is the wireless mode feature on my BT Smart Hub?
The BT Smart Hub allows you to tune your wireless features to give you the best performance with all your wireless devices. Your BT Smart Hub is automatically set to Mode 1.
Mode 1: Gives you the fullest featured wireless, maximising speed and range
Mode 2: Some devices can sometimes struggle to use the latest wireless features. If you have any devices that can’t get a good wireless connection, try using this mode. Selecting this mode may reduce the wireless range and throughput but improve connectivity.
Mode 3: Change to this mode if your wireless devices don’t perform well using mode 1 or 2. Selecting this mode will reduce the latest features as well as wireless range and throughput compared to Mode 1 and 2. It'll enable the broadest range of devices to operate on the wireless. The features that are reduced include: power saving procedures, traffic aggregation methods and Multiple Concurrent data streams
g/n and a/n/ac
b/n/g and a/n
b/g and a
BT's willingness to disable support for older devices by default may explain the problem. On the other hand, I wasn't able to connect my printer (HP Envy) to the Smart Hub even after changing to Mode 2, so the problem could still be elsewhere.