Just found this post after encountering similar problems with my new BT Home Hub 3.
Basically, my printer (a Brother HL-2250DN) is wired to the hub, but I coudn't print to it. The hub also couldn't see the printer, but my Mac could see it (in "Add new printer").
My solution was to delete the printer from the Mac, then perform a factory reset of the printer (you'll need to check your printer's manual). The hub could then see the printer, and I was able to add it as a new printer to the Mac in the usual way.
Through lack of information, I can only assume that the old hub (Virgin Media Superhub), used a different subnet mask to BT's home hub and the printer was unable to change and a factory reset forced it to rescan the entire network.
Hopefully this will work whatever printer and operation system you're using.
Good luck.