The Markit/CIPS construction PMI index eased to 53.6 points from 54.0 points in May, broadly in line with analysts' forecasts of a dip to 53.7 points.
"June data rounds off a further solid quarter of growth, albeit down on the first quarter," Markit economist Sarah Bingham said.
"This contrasts with the surprising weakness seen in the official data for the first three months of the year," she said.
Official statistics showed that construction, which makes up for about 6 percent of economic output, contracted by 3.4 percent in the first quarter, contradicting the expansion signalled by the PMI surveys.
The dip in the construction PMI follows a surprisingly sharp slowdown in the manufacturing industry which fuelled concerns about the health of the broader economic recovery.
The construction PMI showed that commercial and civil engineering companies saw output rising while house building shrank for the second time over the past three months.
"The worry is that the level of business confidence has fallen to a six-month low in the sector, which suggests that companies are expecting growth to weaken over the next twelve months," Markit economist Bingham said.
"That is perhaps not altogether surprising given a marked easing in the rate of expansion of new business inflows in June," she said.
The survey also showed that firms cut back staff as a result of the slowdown in orders.