If you are asking what a brake controller does, then what it does is sense when the vehicle is slowing down (some use an internal accelerometer) and then apply the brake signal to the trailer. It has an adjustment for controlling how hard the brakes are applied...a fully loaded trailer will need heavy braking, while an empty trailer will skid the wheels if too much brake is applied. I don't think there is any Land Rover "recommended" part...and it is probably more a function of the trailer than the tow vehicle anyway. As I mention above, the Tekonsha P-3 is a good choice and should handle any trailer the LR4 is capable of towing. Light trailers do not have brakes so obviously it is of no use with those.
Great explanation! Thanks much!