UPDATE 1-Sterling hits 7-day high as dollar wilts, data beats expectations

* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh

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

LONDON, June 4 (Reuters) - Sterling rose to a seven-day high on Monday as the dollar fell and data on Britain's construction sector narrowly beat expectations.

In May, the pound fell 3.43 percent versus the dollar, its biggest monthly decline since 2016, as weakness in the UK economy and non-UK factors including new U.S. trade tariffs impacted the currency.

However, analysts say sterling could fare better in June if there are signs of the British economy gaining momentum after a sluggish first quarter and if the Brexit talks progress meaningfully.

Sterling rose 0.2 percent to $1.3398 early in Monday's session, helped by broad dollar weakness. It traded down 0.3 percent at 87.69 pence against a resurgent euro.

The euro rallied on relief among investors that the new coalition government in Italy does not intend to head back to snap elections or exit the euro.

A purchasing managers' index (PMI) for Britain's construction sector showed activity at 52.5 for May, the same as the previous month, but higher than 52 predicted by analysts, as the impact of adverse weather dropped out of the survey period.

Investors are studying economic data for signs of whether the Bank of England will raise interest rates to curb inflation this year.

Bad weather and slow growth saw markets in May drastically scale back expectations for monetary tightening by the BoE.

"If the economy gains some momentum in June that will boost the chance of a BoE rate hike in 2018 and fuel further demand for the pound this month," WorldFirst head of FX strategy Jeremy Cook said.

On Friday, a survey showed UK manufacturing growth picking up speed in May. Data on Tuesday is also expected to show some month-on-month growth in the UK's vital services sector.

"A solid services data-point would aid the pound's recovery further as it looks to gain traction after the large declines seen in May from the April highs," said David Cheetham, a market analyst at XTB. (Reporting by Tom Finn; Editing by Gareth Jones)