Twazzockwidget is a portmanteau word made by combining 3 separate words. Twazzock is said to be derived from combining twat in the sense of a general insult with wazzock, a word from the north of England which means a foolish or inept person.
Added to these is the word widget, a general-purpose term for any hypothetical object to give twazzockwidget.
A twazzockwidget is therefore a person, usually one in a position of authority, whose presence somehow causes the level of competency to be lowered in anyone they have dealings with.
"Who's in charge on your nightshift tomorrow?"
"Don't ask, it's that bloody Martine again!"
Oh dear! No matter how well prepared the place is or who else is working, there is always something that goes badly wrong when that twazzockwidget is in charge!"