* 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, Nov 17 (Reuters) - Sterling inched up on Friday, trimming early gains as investors took profits after the European Union repeated an early December deadline for Prime Minister Theresa May to move on Britain's Brexit divorce bill.
European Council President Donald Tusk increased the pressure on May to make progress in time for the EU to respond at a summit on Dec. 14-15, or risk losing a chance to push the talks to a discussion of future trade ties -- something London desperately wants so it can offer some certainty to nervy businesses.
Sterling rose half a percent early on to hit a 2-1/2 week high of $1.3260 amid broad dollar weakness. But the pound gave up most of the gains to stand 0.1 percent higher on the day at $1.3203.
It is set to rise for a second consecutive week.
"Traders don't want to carry any long sterling positions into the weekend due to headline risks around Brexit," said a trader at a U.S. bank in London.
With Britain's autumn budget due next week, markets will trade in broad ranges.
Capital Economics said in a note that flexibility to offer fiscal giveaways was very limited due to a struggling economy.
The dollar slipped to a four-week low against the yen on Friday, after a newspaper report that investigators probing possible Russian interference in the 2016 U.S. election had subpoenaed officials of President Donald Trump's election campaign for documents.
Sterling's tiny gains were also accompanied by a pick-up in implied volatility, a gauge for expected price swings, in the derivatives market indicating the currency remained very sensitive to Brexit headline risk.
Progress between European and British negotiators at the December summit in Brussels is seen as an important milestone in the Brexit talks, as businesses seek clarity on the terms of the divorce by the new year, when many will make investment decisions.
Data this past week offered hardly any support to sterling.
UK consumer price inflation was at 3.0 percent in October, lagging expectations, while the number of people in work in Britain fell by the most in more than two years in the three months to September.
Both indicators would support the view that further interest rate rises by the Bank of England would come at a slow pace.
Against the euro, sterling was broadly flat on the day at 89.29 pence (editing by John Stonestreet)