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UPDATE 1-British pound holds near 3-month highs after construction report

* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Updates with data, quote)

LONDON, Jan 3 (Reuters) - Sterling was flat but still holding near a three-month high of $1.36 on Wednesday, after a survey showed that growth in Britain's construction sector slowed last month.

It was trading flat at $1.3584, having weakened slightly after the survey release.

The pound recorded its best annual performance against the dollar last year since 2009, with an almost 10 percent rise amid broad dollar weakness.

It is still much weaker than before Britain voted to leave the European Union.

Against the euro, sterling was down slightly at 88.62 pence in early trading on Wednesday.

The IHS Markit/CIPS UK Construction PMI slipped to 52.2 after hitting a five-month high of 53.1 in November, the first slowdown in growth since September.

The PMI came in just below a median forecast of 52.5 in a Reuters poll of economists.

Lee Hardman, a London-based currency analyst at MUFG, said the PMI data had little impact on sterling or the bigger picture of the economic growth outlook for the UK. Progess surrounding Britain's negotiations to leave the European Union would continue to shape the direction for the pound, he said.

"We are focusing on Brexit negotiations. We will be looking for signs of progress," Hardman said.

"We think there is a lot of pessimism priced into the pound," he said, predicting a move higher to $1.40 this year.

David Madden, an analyst at CMC markets, attributed the pound's recent strength to dollar weakness, and said "rallies could encounter resistance at $1.3600 or $1.3659". (Reporting by Tommy Wilkes; Editing by Jeremy Gaunt)