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chez_jay
The pi-hole comes on the other side of the router part of your diagram. It can sit anywhere, even over wireless.
Pi-hole works by diverting DNS requests for ad-serving networks to a blackhole - You configure your router to route all DNS requests to the pi-hole.
That means it needs an IP address, which the router provides / deals with.
The Pi-hole wouldn't know what to do with the signal from the wall socket, as it's not a modem , and at the same time, your network wouldn't know where to find it, even if it had the hardware / software to deal with the signal.
The Virgin router is a modem / router / switch / wireless AP combo.