Economists said the positive data raised the chances of stronger second-quarter growth than the 0.3% in the first three months of the year.
The construction PMI rose to 51.0 in June, the highest level since May 2012 and up from 50.8 in May.
Housing construction grew at the strongest rate in June according to the PMI, helped by the government's incentive schemes, although growth slowed to 51.5 from 54.4 on the index.
It was also encouraging to see the commercial and civil engineering and sectors stabilise, at 50.1 and 50 respectively, improving after several months of contraction.
The survey showed that new orders in house building were stronger in June than in May which in turn contributed to creating new jobs in the sector, the first increase in employment since February.
“The improvement in overall construction output simultaneously raises chances of strong second quarter U.K. GDP growth, and reduces the likelihood of imminent additional policy stimulus from the Bank of England.” said Tim Moore, senior economist at Markit.