The closely-watched purchasing managers' index (PMI) for the sector came in at 52.3 for the month of September, comfortably above the 50 score which represents stagnation. It was also above the 49.2 recorded in August and well ahead of the 49 expected by economists.
The score helped arrest the slide in the value of the pound, which had fallen dramatically in the first hour of trading in London. Sterling climbed from $1.2773 to $1.2787 in the minutes after the announcement.
Markit, which compiles the statistics said a "solid rebound in residential [building] was the key factor" behind the strong figures, in an early boost to the government's £5bn housebuilding drive announced by chancellor Philip Hammond at the Conservative Party Conference yesterday.
Tim Moore, senior economist at Markit, said: "Construction companies moved back into expansion mode during September, led by a swift recovery in residential building from the three-and-a-half year low recorded in June.
"Resilient housing market conditions and a renewed upturn in civil engineering activity helped to drive an overall improvement in construction output volumes for the first time since the EU referendum."
Construction firms said concerns over the health of the UK economy in the wake of the surprise Brexit vote had slipped back since June, although signs of inflationary pressures were building, with the cost of imported raw materials rising as a result of the weaker pound.