#PowerShell, <s>70</s> <s>63</s> <s>55</s> 53 Bytes

Excluded double quotes, easy -2 thanks to [@Joey](https://codegolf.stackexchange.com/users/15/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.