He has told Network Rail chief executive Iain Coucher that not enough is being done to ease passenger misery following another week of disruption on the line.
Last week saw horrendously long waits for trains after more than a mile of Network Rail's overhead cables were torn down near Ingatestone.
The chaos started during the Monday evening rush hour, and services got back to normal only on Friday.
As engineers worked to replace cables at Ingatestone commuters endured further disruption when a freight train derailed at Marks Tey at 2pm on Thursday, causing the line to be closed at Witham.
By the evening, one line was opened up but this led to a backlog of trains and had a severe impact on journeys.
Commuters have been hit by a string of major delays since January caused by bridge collapses, over-running engineering works and power problems.
Mr Burns fumed: “The disruption to the Chelmsford–Liverpool Street line in recent weeks, caused by damage to the overhead electric wires, has become unacceptable.
“I believe that, as a matter of urgency, Network Rail should invest in replacing all the outdated electric wires by the end of 2009-10.
“I hope that Network Rail will look into this in a positive and sympathetic way because something has got to be done to ensure a reliable service for Chelmsford commuters who depend on the railway to get to work in London or to travel to London.”
A Network Rail spokesperson said: “Network Rail is committed to the Anglia region and is investing £150m in renewing 30 miles of overhead power line between Liverpool Street Station and Chelmsford.
“Work on this important upgrade project began earlier this year and, given its size and complexity, is due for completion by 2012.
“It would not be in the best interest of commuters for us to accelerate these works, as it would mean closing the line for a long period of time, which in turn would cause major disruption to services.”