You can transmit HDMI signal over a wifi connection but would need to purchase a hdmi sender, or alternatively you can purchase long HDMI cables depending on the distance, I have used 10m cables with no issue. 10m Cable option would cost approx 10 pounds or a hdmi sender/receiver will cost from 70 pound.
Another option would be get virginmedia to extend you coax cable for the TIVO box only to the TV cost 99 pound.
I dont work for VirginMedia all opinions are my own. 39 years in IT.
-------------------- Services: HD TV on VIP (+ Sky Sports & Movies & BT sport), x3 V6 boxes (1 wired 2 WiFi,) SH2 in modem mode with Airport Extreme Router. On VIVID200, Talk Anytime Phone, x2 Mobile SIM only iPhones.