Companies polled for the survey pointed to the double Bank Holiday in June as being partly to blame, but firms also referred to what Markit called "weaker underlying conditions" and "worsening economic conditions".
Civil engineering and housing activity were the worst performers, seeing a drop in output for the first time since weather-hit January.
Encouragingly the survey found that “on balance” construction firms expected an increase in business activity over the next 12 months, although the level of positive sentiment “remained well below the long-run survey average”.
Markit/CIPS said that reports from companies contributing to the survey “frequently cited concerns about the weakening business outlook as having dampened their forecasts for output over the year ahead”.
The snap-shot of UK construction followed another survey by Markit/CIPS which concluded that conditions in the country’s manufacturing sector remained “fragile”.
“June saw manufacturing production rise for the sixth time in seven months, but only following a solid contraction during May,” authors of the survey said.
The Markit/CIPS Manufacturing PMI rose to 48.6 in June, from 45.9 in May, but remained below the ‘neutral’ figure of 50.
Problems in the eurozone continued to hit new export orders last month, and overseas demand was reported by the survey to have fallen for the third month in a row, albeit by the least amount during the period.