to "Go off like a Cumbrian Taxi Driver" is another way of saying "to Go apeshit"
The phrase originates from the 2010 case where taxi driver Derrik Bird went on a murderous rampage through Cumbria, killing twelve innocent people and injuring a further eleven. Apparently, the cause for his psychotic behaviour was a relatively minor annoyance - caused by drivers taking fares from the wrong end of the taxi lane.
Typically speaking, "going off like a Cumbrian taxi driver" is to overreact to a relatively minor annoyance, normally with extreme anger.
Hey, man... I said I'm sorry.... No need to go off like a Cumbrian Taxi Driver!