The fired trio worked for Armstrong subsidiary ACP (Concrete) Ltd at the firm’s precast production plant in Workington.
Several workers were found to have drugs in their systems following random tests in November for cocaine, cannabis and amphetamine.
All were given counselling and the company waited 13 weeks before testing them again.
Group security manager George Nevins said the gap between tests was to give them a chance to clean up their act and to allow all trace of the original drugs to leave their system.
But three manual workers tested positive again in February and were dismissed last week after a disciplinary hearing.
Nevins told the News & Star: “The first test was in November when a number of random people were picked out.
“Some of those tests were positive and the company offered those individuals the support they needed to try to break their habits.
“We did inform them that they would be tested again some time in the future but this was not pre-arranged.”
Keith Denham, chief executive of Thomas Armstrong, stressed said the company had a zero tolerance to drugs.
He said: “We carry out manufacturing with machinery. It’s a dangerous operation and we have to have people in a role where nothing affects their performance. You can’t have people not fit for work.
“We have to run a safe operation and we can’t have people with habits like that.
“If you do that for a long time, eventually you are going to get caught. We can’t condone it.
“If there was an accident [because workers had taken drugs] we would be in serious trouble.
“We are shocked because they have lost their jobs but they had their final warning in January but continued to use the drugs.”