The process will often involve builders disclosing to one another what price they intend to quote.
Kier Group was fined £17.9m, more than any other building firm.
Interserve was fined £11.6m, while other companies fined more than £5m were Galliford Try, Ballast Nedam, Bowmer & Kirkland, ISG Pierce and Crest Nicholson, John Sisk & Son, Connaught, Carillion JM, Concentra and Durkan Holdings, and Balfour Beatty.
Balfour was fined £5.2m for practices that took place at subsidiary Mansell before its acquisition, the company said.
"In light of the investigation, Balfour Beatty carried out a thorough and detailed audit of all its businesses to ensure that it is fully compliant with all aspects of competition law," it said in a statement.
Carillion, which was fined £5.4m, said its punisihment related to contracts tendered by Mowlem, which it bought in 2006.
"The decision does not involve any other business within the Carillion group," it added.
Meanwhile Galliford Try, fined £8.3m, said it was that it was not found to have made any financial gain, and the eventual price paid by the client had not increased.
Alan Ritchie, general secretary of construction union Ucatt, said: "It is clear that construction companies can't be trusted to run their affairs properly.
"A zero tolerance approach must be taken with the construction industry to ensure that companies follow the law."
The UK Construction Group, which represents 29 contractors, called the decision to penalise the firms "unfair".
Deborah Jones, OFT: "It's a breach of competition law"
"Everybody knows - including the OFT - that cover pricing was widespread in the industry in the past," said the body's director Stephen Ratcliffe.
"It is perverse and unfair to impose such disproportionate penalties on a small number of contractors selected by geographical sampling."
Adam Aldred, competition partner at law firm Addleshaw Goddard, which represents five of the firms investigated, said the OFT was the first competition authority in Europe to rule against building firms for the practice of cover pricing.
In 11 instances investigated by the OFT, the body found that the lowest bidder faced no competition because all other bids were cover bids.
It also found six instances where successful bidders had paid an agreed sum of money to the unsuccessful bidder. These payments were between £2,500 and £60,000 and were made using false invoices.
The infringements affected building projects across England worth in excess of £200m, including schools, universities and hospitals, between 2000 and 2006.
The OFT said that 83 out of the 103 firms had received reductions in their fines because they had already admitted the practice.
"Our investigation has uncovered significant infringements of competition law on nearly 200 projects across England," said Simon Williams at the OFT.
"Bidding processes designed to ensure clients and in many cases taxpayers receive the best possible choice and price were distorted, creating a real risk of increased prices."
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