Yes HomePlugs are connected by Ethernet cable (supplied with the plugs). One starts with a Pair of Homeplugs, one is connected to the Router and to a handy Mains Socket - the other is connected to any convenient Mains Socket in the home (on the same Ring Main) and to the other PC etc.
I use HomePlugs, mainly for when friends bring me their Laptops to work on, makes connection to Internet extremely simple and immediate.
"Neither of the adapters sees any network at all."
If the adapters are configured for the North American market, and your router is broadcasting on wireless channel 12 or 13, then that could account for why your router is invisible to those adapters. In North America only channel numbers 1-11 are valid, while in the UK ours go up to 13. Having said that though, when you install the adapter software it usually asks which country you're in and configures itself appropriately. Here's what you can try though:
Login to your BT Home Hub and go to its wireless section. Make sure that the wireless channel number that it's using is 1 to 11. Don't forget to save any changes you make.