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Sterling sinks against euro, flat against battered dollar

* 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, Aug 29 (Reuters) - Britain's battered pound sank to 11-month lows against the euro on Tuesday as the single currency rose across the board, as political uncertainty elsewhere drove investors in search of relative safety.

It was flat against the battered dollar at $1.2926.

The euro has gained from weakness in both currencies.

It crossed through the $1.20 threshold for the first time in 2-1/2 years, benefiting from broad risk-off move as geopolitical tensions escalated following a missile launch over Japan from North Korea which dented the dollar.

The euro has also been boosted by political uncertainty in Britain, with its exit from the European Union hitting UK growth and keeping the pound weak while growth picks up in the euro zone. It slipped to 93.07 pence per euro on Tuesday, its weakest since early October.

"You've got two politically plagued currencies offsetting each other youve got Brexit for sterling and you've got Trump and geopolitics for the dollar," said ING currency strategist Viraj Patel.

"So in effect the euro is the de-facto political haven. Cable (sterling/dollar) is caught in the crossfire of what's happening in the euro and dollar," he added.

Patel said the pound's weakness against the euro had become "a bit excessive", and that Brexit risks were already priced in.

Analysts say sterling's recent moves against the dollar and the euro have largely been a result of broader shifts in the dollar as investors worry about the ability of the U.S. administration to follow through on its economic agenda.

Investors also had their focus trained on the third round of Brexit negotiations which started on Monday, with the European Union's chief negotiator saying he was concerned at the slow progress of the talks.

The British government has laid out a series of position papers that have outlined compromises over some of the issues likely to block progress in talks this year, but EU officials say Britain needs to settle its divorce bill with the bloc before a trade agreement can be discussed.

"We've been seeing a bit of back-and-forth about the requirement to finalize divorce terms before negotiating a trade deal or beginning that negotiation," said Caxton FX analyst Alexandra Russell-Oliver.

"That could put some downward pressure on the pound."

(Reporting by Ritvik Carvalho and Jemima Kelly; Editing by Jeremy Gaunt)