Sharp falls in commercial building work and in civil engineering activity meant the latest Markit/CIPS purchasing managers' index (PMI) measuring overall output in the sector declined to 46.8 from 48.7. It means the headline index has been below the no-change in activity value of 50 for four months running.
The UK economy's miserable winter continued after figures showed the construction sector endured its worst month since October 2009 in February.
CIPS chief executive David Noble said there was "barely a crumb of comfort" in the figures, which have added to pressure on Chancellor George Osborne to come up with measures to boost the economy in this month's Budget.
Mr Noble said: "The dramatic fall in civil engineering activity is particularly worrying, having been the one bright spot in the second half of 2012."
The housing sector registered mild growth for the first time in nine months but it remains weak compared with its long-term average.
The prospects for construction firms also appear gloomy, with survey respondents highlighting a deteriorating picture in new orders and lower levels of new work for each month since last June.
The construction update and Friday's poor PMI figures from the manufacturing sector increase the prospect that the Bank of England will announce more economy-boosting measures at its monthly meeting this week.
Sterling has taken a hammering in recent weeks, with Moody's decision to strip Britain of its prized AAA rating last Friday among negative factors. It was worth 1.50 against the US dollar, a two-and-a-half-year low.