The survey, published yesterday by the Chartered Institute of Purchasing and Supply, also showed employment in the sector rose for a 12th consecutive month.
This is the longest period of continuous job creation recorded by CIPS's construction survey, which is compiled by financial information company Markit, since that between mid-2006 and early 2008.
Rates charged by sub-contractors in May increased at the fastest pace in the 17-year history of the survey. Availability of sub-contractors fell at the fastest pace since August 1997.
CIPS's purchasing managers' index for construction, which measures activity in the sector, fell from 60.8 in April to 60 in May on a seasonally-adjusted basis, but remained well above the level of 50 which separates expansion from contraction.
Housebuilding activity remained the strongest-performing construction sub-sector in May, CIPS noted. The slowdown in overall sector growth in May resulted from an easing in the pace of expansion of the commercial property construction sub-sector.
Civil engineering activity rose in May at a robust pace, and at a faster rate than in April, the survey showed.
David Noble, chief executive officer of CIPS, highlighted a sharp rise in supplier lead times in May amid stock shortages and supply-chain bottlenecks, as well as the decline in availability and rise in rates of sub-contractors.
Mr Noble said: "Consequently, with supply constraints still persisting, there are some concerns about how this prolonged period of growth can be sustained over the course of 2014."