The headline activity index rose to 56.5 in February from 53.7 in January, confounding analysts' forecasts for a fall to 52.9.
The construction sector suffered a sharp downturn at the end of last year, partly due to the worst December weather in a century, but Markit said February's data suggested there would be a bounce-back in the first quarter of this year. The survey showed that all three construction sectors recorded growth last month, with civil engineering enjoying the strongest expansion in three years.
Homebuilding also increased and commercial building continued growing for the 12 successive month.
"The situation is still fragile, however, considering the likely impact of government cuts," said David Noble, chief executive at the Chartered Institute of Purchasing & Supply.
"Concern about the level of bank lending is also having a negative impact on confidence. This is echoed by a further reduction in employment." Construction firms continued to shed jobs, but at their slowest pace in 8 months and the survey said some companies had reported they were taking on staff to cope with higher workloads.
However, input costs rose at their fastest rate since August 2008, driven by oil, fuel and steel.