PowerShell, 70 63 55 53 Bytes

Excluded double quotes, easy -2 thanks to @Joey

for(){cls;(date 31Mar19)-(date)|% T* ddd\:hh\:mm\:ss}

Running this with sleep adds 8 bytes, but the input is mostly invisible if it is run without them, version (63 bytes) with sleep:

for(){cls;(date 31/3/19)-(date)|% T* ddd\:hh\:mm\:ss;sleep 1}

for() is an infinite loop, and within that loop..

cls to clear the screen,

get 31/3/19 as a DateTime object, and - the current date from it, to give the time remaining, then .ToString() (|% T*) that with the correct format.

this will display negative time after brexit.