The closely-watched Markit/CIPS UK construction purchasing managers' index (PMI) showed the volume of new work fell for the eighth month in a row in November - marking the longest phase of decline since 2013.
It signalled activity overall in the sector contracted once again last month, but at the slowest pace for four months.
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The PMI recorded a reading of 45.3 for November, up from 44.2 in October.
A reading above 50 indicates growth while one below that represents contraction.
This was the slowest pace of decline since July, though the PMI reading has shown output falling for seven consecutive months now.
Economists cautioned the sector's performance fuels fears over a difficult final quarter for the wider economy.
British companies have been selling their foreign assets at the fastest rate since the start of the century, new officials figures revealed on Tuesday.
The number of outward disposals, where British companies sell off a majority stake in a foreign subsidiary, hit 23 over the third quarter of 2019, data from the Office for National Statistics (ONS) showed.
The combined value of these deals were £10.1 billion, the highest since the same three-month period in 2000, when deals hit £15.3 billion, the data shows.
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It came as a weak pound helped British companies, selling assets in dollars or euros, get a bigger return due to favourable exchange rates.
The figure is also a rise of £9.3 billion from the previous quarter, when deals only reached £0.8 billion, the data shows.
Meanwhile, the value of inward mergers and acquisitions (M&A), where foreign companies based abroad buy British ones, fell by £8.5 billion from the quarter before to £10.1 billion in the last three months.
Shareholders in Premier Inn owner Whitbread should vote against a new pay package for its top executives, according to an influential advisory group.
Proxy adviser PIRC joined another advisory group, ISS, calling for shareholders to vote against the new proposal, which could hand executives bumper bonuses.
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The proposal has been backed by Glass Lewis, another such group.
If shareholders pass the new system at a meeting on Friday they could be handing chief executive Alison Brittain more than four times her annual salary in total pay from the next financial year.
Her remuneration will be based on if she can meet certain targets set out by the board.
"The total potential awards under all incentive schemes are considered excessive at 325% of salary," PIRC said in a note to shareholders.
"Based on these concerns, an oppose vote is recommended," it added.
Last year, Ms Brittain pocketed nearly £3.7 million from the sale of Costa, the company's coffee chain, to Coca-Cola for £3.9 billion. This brought her total pay to nearly £5.6 million.