Profit at Laing O'Rourke has grown from £7.8m in 2000 to £45.7m last year, when the company was 16th in the list.
The next nearest contractor was Midas Group of Bristol, which reported a 65% profit growth to £4.2m in 2003. It was 40th overall.
Midas chairman and chief executive Steve Hindley attributed the growth to the success of his five-year plan to grow the firm's profit margin from 1% to 3% – a target it has now hit.
He said this was done by focusing on building long-term work with repeat clients rather than competitive tendering.
Hindley said: "We have put together customer focus teams. For example, our Marks & Spencer team does nothing but Marks & Spencer work. We are hoping to exceed the 3% margin this year."
The best performing firm linked to the construction sector was Cumbria-based rail engineer and housebuilder WA Developments, which was placed at number nine.
We are hoping to exceed the 3% margin this year
Steve Hindley, Midas chairman
An increase in rail repairs work was partly responsible for the 114% surge in profit growth to £5.9m in its last annual results.
Housebuilders fared particularly well, with 12 listed. Strata Group, of Doncaster, was the second fastest growing, finishing in 18th place with a profit of more than £11.4m.
Irving Weaver, chairman of Strata, said that the company had benefited from following government guidelines on increasing the density of its developments. Weaver said improving the design of the company's homes had boosted profit, with average selling price increasing from £93,000 in 2002 to £133,000 last year.
He said: "We introduced a new range of housing two years ago this month and this has fed through to the results."
Weaver added that Strata will look to build more than 320 housing units this year, up from 262 in 2003. This will help to increase turnover from £57m to an estimated £68m this year.