The BT TV Box Pro and BT TV Box Mini will work without an aerial connected, but you'll miss out on some free-to-air channels, including Dave. You can check which channels are available here.
If you do not have an aerial then you will need to connect your BT TV Box to broadband in order to watch free-to-air channels and On Demand content. BT TV Boxes can be connected to your broadband either by wi-fi or Ethernet cable. We recommend the use of Ethernet cable for the best experience. There will be an Ethernet cable included in your box.