The Markit/CIPS Purchasing Managers' Index (PMI) for the sector rose to 58.1 in June from 55.9 in May. A reading above 50 indicates expansion.
Markit added that confidence in the sector about the coming 12 months was at its highest for 11 years.
Residential house building remained the fastest growing area in the construction sector.
Looking ahead, nearly two-thirds of construction firms expect to see a rise in their activity as a result of increased investment spending among developers and robust demand for new residential projects.
Construction firms are also hiring staff at the fastest pace in six months the survey found.
Tim Moore, senior economist at Markit said the extent of the recent rise in construction optimism was "partly down to relief that pre-election uncertainty has now passed".
He added that the rise in output also suggested firms were confident that underlying demand would continue to recover.
Earlier in the week, the Office for National Statistics (ONS) revised UK economic growth for the three months to March up to 0.4% from an original estimate of 0.3%, based on stronger than previously calculated activity in the construction industry.
The upbeat construction survey contrasts with the Markit/CIPS PMI reading for the manufacturing sector, which indicated growth slowed to its lowest pace in more than two years in June.
The manufacturing PMI reading fell to 51.4 in June from 51.9 the month before.
Markit's survey for the UK's services sector is due to be released on Friday.
Activity in the UK's construction industry grew last month at its fastest pace since February, a survey suggests.