Markit Economics said the sector's PMI, which climbed from contraction to expansion in May for the first time since October 2012, pushed marginally higher with headline index climbing from 50.8 to 51.
Numbers in the index above 50 indicate business growth.
Markit said the index rose "fractionally."
"Although the construction sector faces a long and fragile road to recovery, June's survey highlights a nascent turnaround in optimism about future output levels in the sector," Markit Senior Economist Tim Moore said in a statement.
"House building remains the mainstay of growth, helped by government incentive schemes, while it was also encouraging to see civil engineering and commercial building stabilize after protracted declines in 2013 so far," he said.
David Noble, chief executive officer at the Chartered Institute of Purchasing & Supply called the recent upswing "a new dawn" for the construction industry.
"A new dawn is emerging ... with confidence of a sustained recovery beginning to build thanks to two months of consecutive output growth and the pace of new orders expansion hitting a 13 month high," he said.
"Housing is the leading light sustaining last month's performance, meanwhile commercial and civil engineering activity stabilized, arresting months of decline, giving further cause for optimism," he said.