The PMI rate for the sector was 48.7 in January, showing no change from December.
Lower construction output in January indicates declining housing and civil engineering activity, while a fall in civil engineering was the first since August 2012.
The majority of respondents cited weak underlying client demand and a lack of new projects.
Volumes of commercial activity remain unchanged, ending a five-month period of contraction.
January showed an eighth, consecutive monthly fall in new business intakes across the construction sector.
This made it the longest continuous period of decline since 2008/09.
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Decreased new order volumes and lower output contributed to another reduction in input buying in January.
Supplier performance also showed a sharp fall, with vendor delivery times lengthening to the greatest degree in three months.
But there has been an upturn in confidence regarding the outlook for business activity over the next 12 months. The latest reading was the highest since last July.
Tim Moore, senior economist at Markit and author of the Markit/CIPS Construction PMI, said: "January’s survey results are yet another indicator of the severe underlying fragility across the UK construction sector, with output failing to rise in any of the three monitored sub-sectors for the first time since last summer.
"Snowfall at the start of the year may have disrupted output to some degree, but unfavourable weather outside is clearly far down the long list of difficulties afflicting construction companies at present. Weakness was again most prominent within the house building sub-sector during January, while civil engineering swung back into contraction after a four-month period of growth.
"Despite the ongoing downturn in output, there was some let up in the pace of new order decline, as well as a resilient employment trend in January. Looking ahead, construction firms reported improved optimism about the business outlook, although much of this appeared to rest on hopes that the chorus of calls for greater public sector investment spending starts to come to fruition."
(IT)
