* 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 (Recasts, updates prices, adds comment)
LONDON, June 2 (Reuters) - Britain's pound hit a 2-1/2 month low against the euro on Thursday as a weak U.S. jobs report prompted broad selling in the dollar and gave Europe's shared currency a lift.
Investors took the view the report showing the U.S. economy added fewer jobs than expected last month could derail a possible interest rate hike by the Federal Reserve in the second half of this year. That saw broad buying into the euro, which pushed the pound lower.
The pound fell as much as 0.6 percent to 87.67 pence per euro, its lowest since March 14. It was half a percent lower at 87.47 pence per euro by 1617 GMT.
As the dollar came under pressure, the pound rose 0.1 percent to $1.2884, moving into positive territory.
"We saw bit of a pop higher in the pound versus the U.S. dollar following the weaker U.S. non-farm payrolls earlier but that's faded back somewhat," said David Cheetham, chief markets analyst at online broker XTB.
Earlier, data showed British construction activity grew at its fastest rate since the end of 2015 last month. The Markit/CIPS construction purchasing managers' index (PMI), jumped to 56.0 from 53.1, its highest since December 2015 and above all forecasts in a Reuters poll.
But sterling shrugged off the data, as polls predicting a wide range of outcomes - from a slim majority for Prime Minister Theresa May's Conservatives to a hung parliament - have kept investors focused on Britain's election next week.
While sterling has kept its gains of nearly 4 percent against the dollar since May called the election, in trade-weighted terms it has lost nearly all of the boost it got after the announcement.
That it has kept some of its gains against the dollar has some investors sounding warnings.
"Even after recent falls, markets appear to be pricing in a Conservative majority of around 85 seats on June 8. While this is down from a peak of 160, it is still larger than an objective reading of recent polls would suggest," analysts at RBC Capital Markets wrote in a note to clients.
"The longer-term implications of the election are more ambiguous, but sterling's preference for a larger expected Conservative majority is clear in the short term and the risk is that both fall further." (Reporting by Ritvik Carvalho; Editing by Andrew Bolton)