The Markit/CIPS construction PMI headline activity index fell sharply to 50.1 in September from 52.6 in August, its lowest reading since a contraction in December 2010.
The weak construction figures contrast with surprisingly solid growth from the manufacturing sector in September, and come at a delicate time for Britain's economy as the Bank of England considers whether to start a second round of quantitative easing.
"Activity growth slowed to near-stagnation, with constructors relying on work on existing contracts to support output. This therefore bodes ill for construction activity in the coming months," said Sarah Bingham, an economist at Markit.
"UK construction companies continued to struggle in the face of growing concerns about the wider economy, with weaker client confidence leading to a reduction in new business received during September," she added.
A sluggish housing market has dented the appetite for new residential construction, while government spending cuts have reduced the public funds available for civil engineering projects.