While a quarter saw no problem with discussing bids and agreeing who would get which tenders.
The shock findings follow research by the Competition and Markets Authority (CMA) as it launched a new campaign targeting anti-competitive practices.
The survey also found that only 6% of 400 construction firms quizzed had received competition law training while 32% thought agreeing not to supply each other’s customers was legal.
A crackdown on illegal cartels saw the CMA issue £43m in fines last year alone.
Howard Cartlidge, the CMA’s Senior Director of Cartels, said: “The CMA is cracking down on businesses that collude to rip off customers by fixing prices, sharing out markets amongst themselves or rigging bids.
“Our message to them is that we know cheating when we see it, even if you don’t.
“Pleading ignorance is no defence; it’s up to businesses to know what these unfair practices look like and avoid them.
“By ensuring you stay on the right side of the law, you can avoid substantial fines, director disqualification or jail.
“And if you suspect something illegal is going on, report it to us before it’s too late.”
Businesses found to have been involved in illegal cartels can be fined up to 10% of their annual turnover.
Individuals can face up to five years in prison and directors can be disqualified from holding director positions for up to 15 years.