The latest Markit/CIPS UK Construction Purchasing Managers' Index (PMI) registered at 45.9 in July, down from 46.0 in June.
The reading signals the fastest overall decline in output since June 2009.
Anecdotal evidence suggested that economic uncertainty following Brexit was the main factor contributing to business activity in July.
In addition, new work declined for a third month running. However the rate of deterioration slowed and was close to that seen in early 2013.
While investors who took a "wait-and-see" approach to decision making, there were reports that overall demand had been "relatively resilient" in July.
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David Noble, Group Chief Executive Officer at the Chartered Institute of Procurement & Supply, said the marginal drop in is a "seriously disappointing development".
"The index also recorded the lowest business confidence since April 2013, and the fastest overall fall in output since June 2009. Commercial building bore the main brunt of this downturn with the largest decrease in activity for six-and-a-half years," he said.
"Material costs were driven upwards at the fastest pace since March 2015, with the weaker pound largely to blame, and some firms reported lower stock levels to maintain cash flow. Job falls were in evidence, but more as a result of a close watch on margins and natural shedding than a shrinking of operations.
"With a reduction in new work for the third month in succession and one of the fastest falls since early 2013, this hesitancy to commit was largely attributed to the continued hazy gloom of uncertainty as clients became more cautious, and deferred orders. The picture is still unclear around whether this direction is fixed for the coming months or is a short-term reaction and the aftershock of the UK's referendum decision."
(LM/CD)
