A public inquiry into Grittenham Haulage Ltd resulted in the ban being imposed in December 2015.
The decision has now been made public following the conclusion of the trial.
Matthew Gordon, 30, and Peter Wood, 55, were found guilty of manslaughter in December 2016.
Mitzi Steady, four, Robert Parker, 59, Philip Allen, 52, and Stephen Vaughan, 34, died in the crash in February 2015.
Gordon, of Dauntsey, Wiltshire, was the owner of Grittenham Haulage Ltd and was driving in a truck in front of the lorry that crashed.
Wood, of Brinkworth, Wiltshire, was a mechanic employed by Gordon who carried out safety checks on the truck.
The driver of the crash truck, Phillip Potter, 20,  also from Dauntsey, was cleared of dangerous and careless driving.
Traffic Commissioner Sarah Bell also disqualified the firm and Mr Gordon from holding or obtaining an operator's licence for two years.
Miss Bell said: "This is a breach of trust of the highest order.
"The operator put commercial concerns first with compliance a poor second until February 2015.
"Failing to observe the rules, not setting aside proper time for quality management and control of the transport operations, running more vehicles than authorised and seeking to keep clients serviced regardless of the law, strikes at the heart of the underpinning principles of the licensing regime, road safety and fair competition.
"After February 2015 the improvement is there but not sufficient to save this licence.
"This is one of those cases that where what happened previously is so serious that the position as at September 2015 is far from sufficient to save this licence. "
Gordon and Wood are due to be sentenced on 27 January.
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