All getting a bit technical.
“emmie, you don't need a landline if you have Virgin Media broadband.”
Depends how you define “landline”. Virgin Broadband works over their own fibre optic landline system. You don’t need a BT landline and you don’t need a phone on the end of it, but you need wires (or more properly, fibre optic cable) to your house.
“Sky provide broadband without a landline,…”
Same again. Sky Broadband actually uses BT’s (or more properly Openreach’s) network. It suffers the same disadvantage as BT’s own Broadband in that, although BT has invested heavily in “Fibre to the Cabinet” (Fibre Optic cable from the telephone exchange to the green distribution cabinets you see in the road) the last bit of the route (from the cabinet to the customer) is usually over copper wires. This restricts the speed and the greater the distance from the cabinet to the premises the lower the speed that can be achieved. As well as this, in order to overcome some of the difficulties caused by using copper (principally slow speeds), BT’s system is “ADSL” (Aysmmetric Digital Subscriber Line). This means that the transmission capability is different in each direction, with the traffic from the exchange to the customer enjoying a much higher transmission speed capability than that from the customer to the exchange.