LONDON (Reuters) - British construction output fell sharply in May during the run-up to the vote on European Union membership, suggesting the sector may drag on economic growth in the second quarter.

The Office for National Statistics said construction output, which makes up 6 percent of the economy, fell 2.1 percent in May compared with April, when it increased 2.8 percent increase.

Economists polled by Reuters had expected a 1.0 percent decrease in May in the often volatile figures.

Overall the figures added to signs that construction struggled as the June 23 referendum neared.

The vote to leave the EU sparked fears of recession and raised deep uncertainties about Britain's future trading relationships, sending the pound to its lowest level against the U.S. dollar since the mid-1980s.

The ONS said construction output would need to expand 1.9 percent in June to avoid dragging on economic growth in the second quarter - something that looks unlikely, according to private sector surveys.

"The fall in May 2016, taken together with the strength of April's figures, continues a longer trend of broadly flat output growth since the start of 2015," the ONS said.

Construction output fell 1.9 percent compared with May 2015. Economists polled by Reuters had expected a 3.5 percent annual decline.

Britain's economic growth slowed to 0.4 percent in the first quarter, compared with the previous three months, according to recent estimates that showed the much larger services sector and household spending were the main drivers of growth.

Financial firm Markit said the construction industry suffered its worst contraction in seven years in June as concern grew about the EU referendum.

Housing construction output fell 3.2 percent in May after edging down 0.1 percent in April, the biggest drop since February 2014.

Housing output has now fallen in every month this year apart from February, and things could slow further after last month's Brexit vote.

The result had an immediate impact on Britain's housing market, according to the Royal Institution of Chartered Surveyors. It said buyer interest and expectations of future sales withered at the fastest pace in years.

Separate ONS figures showed the volume of goods exported fell 11.0 percent in May, the biggest month-on-month fall since July 2006, while import volumes declined at the fastest pace since August 2014.

The trade volume figures had been due to be published alongside the standard cash value figures on July 7, but were delayed to complete quality assurance checks.

(Reporting by Andy Bruce and William Schomberg)