The men who died were Ronald Hill, 38, of Glasgow, Jeff Williams, 42, of Newport, Isle of Wight, Andrew Rogers, 40, of Middlesbrough and Paul Stewart, 23, of Newcastle upon Tyne.
Costain was fined £250,000 after it admitted that it failed to protect its employees properly. Yarm Road was ordered to pay the same amount after it admitted similar charges.
The four men, who had been removing and replacing beams in the bridge, were moving the gantry when the incident took place. The court was told that the mechanisms in place to curb the movement of the gantry were inadequate.
The accident could and should have been prevented
Mr Justice Owen, Bristol Crown Court
Mr Justice Owen, who passed sentence at Bristol Crown Court last Friday, said there had been a disregard for basic health and safety legislation over a long and sustained period of time.
He said: "This is a case of great gravity. Perhaps the most tragic feature of this case is the accident could and should have been prevented by a number of simple measures."