* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1
* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv
LONDON, Jan 8 (Reuters) - Sterling climbed to a three-week high against a broadly weaker euro on Monday, after a cabinet reshuffle alleviated a little of the political uncertainty that has pressured the UK currency in recent months.
Prime Minister Theresa May named a new head of her ruling Conservatives on Monday, among other changes aimed at handing her government a new start after months of divisions over Brexit, scandals and an ill-judged election, which have all weighed on the pound.
Having earlier traded down on the day against the dollar, sterling recovered to trade flat at $1.3565, around a cent away from last week's 3-1/2-month high.
Against the euro, sterling strengthened half a percent to 88.27 pence.
Many investors said that while the reshuffle had removed some uncertainty, it would be unlikely to have a long-term positive influence on the pound.
"You might be seeing some shorts (positions) being covered but we don't think this is a new direction for sterling. The big picture here is that the market has put too much emphasis on the positives from the Brexit developments," said Steven Saywell, a multi-asset specialist in BNP Paribas' sales team.
Saywell said even what was dubbed as a "Brexit breakthrough" late last year, when May secured a deal with the EU that allowed talks to move on to discussions of a transition deal and post-departure trade, did not remove much political risk.
"In reality, we haven't had any breakthroughs at all. All that's happened is that late last year we had a deal that meant things would continue to move on," he said, adding that his view was that sterling would be vulnerable in coming weeks and months.
The currency has been trading between $1.30 and $1.36 since September, and traders say it will take major new developments in Brexit discussions - or a run of strong economic data that brings the timing of the next Bank of England interest rate hike forward - for the currency to break out of that range.
A market gauge measuring expected volatility in sterling was trading at a more than a three-year low, with investors seeing risks around Brexit as fading and betting, therefore, that big price swings would be unlikely in the coming months.
Positioning data on Friday showed speculators added to their bets on sterling strengthening in the week up to last Tuesday, but those positions are still only just in positive territory.
"If we get bad news or good news, markets are going to be in a holding pattern. It's going to take a lot of good news - be it economic or political - to push positioning definitively towards the long or short side," said UBS Wealth Management currency strategist Geoffrey Yu. (Reporting by Jemima Kelly, Editing by William Maclean and John Stonestreet)