As a curious layman I'm intrigued as to what the driver would have known or realised about the split? Did they stop because of no power in their half? Would brakes immediately kick in? Etc etc.
The driver would "loose everything". The emergancy brake would apply and he would loose traction interlock. This is due to wires which run through the entire train ensuring all safety systems are ok. So a passcom being pulled, the air pressure dropping dangerously low, doors being opened on the move, a train splitting etc would all break the wire and cause the emergancy brake to apply and in some instances like a train splitting, also cause interlock to be lost.
A driver has to make certain checks after an unsolicited brake application such as checking the air gauge, TPWS indicator, interlock light and also looking out the window. If the driver can't confirm by looking that he can see the entire train to be complete then the worst has to be assumed and the alarm is raised as it could be blocking another running line.
After the potters bar crash, the first the driver knew something was up was when he lost brakes and interlock and looked out the window to see if the train was complete...