* 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
LONDON, Sept 4 (Reuters) - Sterling slipped half a percent against the euro on Monday, with the single currency rallying broadly as worries over North Korea drove a move away from riskier assets, and as domestic political uncertainty kept the battered pound under pressure.
Data showing growth in Britain's construction sector hit a one-year low in August - hurt by an investment slump in the commercial sector as Brexit uncertainty weighed - had little effect on the currency. Analysts said Tuesday's data from the dominant services sector would be more important.
Data on Friday showed speculators added to their bets against the pound in the week up to last Tuesday, on the back of weak data as well as uncertainty about Britain's departure from the European Union.
Prime Minister Theresa May warned lawmakers over the weekend that Britain could be faced with a Brexit "cliff edge" if they failed to back her EU repeal bill, which is to be debated in parliament on Thursday.
"If we manage to get through this bill without any major hiccups, you would expect sterling to get a bit of reprieve from that," said ING currency strategist Viraj Patel. "(But) I wouldn't read too much into all the Brexit stuff that's going on this week - there's going to be a lot of noise."
May failed to win a clear mandate at a snap election in June and only has a slim majority in parliament that rests on an agreement with a smaller party. She remains vulnerable if pro-European lawmakers in her Conservative party team up with other parties to vote down legislation or support amendments.
On Saturday, May's deputy advised Conservative lawmakers against doing anything that would increase Labour's chances of returning to power, while May said the bill was the best way to ensure a successful Brexit.
"This is a major test for PM Theresa May," wrote Morgan Stanley analysts in a note to clients. "Our economists...still seeing a high likelihood of a general election as Brexit talks finish in late 2018."
Against a dollar that was weaker across the board, sterling was roughly flat at $1.2946.
It was down 0.5 percent against the euro at 92.03 pence , with markets in risk-off mode following Sunday's news of North Korea's sixth and most powerful nuclear test, which prompted the United States to warn of a "massive" military response if it or its allies were threatened. (Reporting by Jemima Kelly)