There are two communication lanes here - let's call them uplink (UAV to satellite) and downlink (satellite to UAV). For the uplink, the UAV can use a highly-directional antenna that is virtually undetectable and unjammable to anyone on the ground.
Solving this for the downlink is harder. Blanketing a large area (100km * 100km) or using highly-directional signal could work. Dead-reckoning with "mission plans" would also help.
I wouldn't really expect BBC to get into technical details, especially given that security-through-obscurity would work for at least the first mission.
