* 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 (Adds new quote, details, updates prices)

By Saikat Chatterjee and Jemima Kelly

LONDON, July 18 (Reuters) - Sterling fell against the dollar and euro on Tuesday, after data showed British inflation unexpectedly slowing for the first time since October last year, lowering expectations of an interest rate increase this year.

The pound jumped last month when various members of the Bank of England's monetary policy committee - including the governor himself - hinted that rates could rise in the coming months.

But the bank has also made clear that any monetary tightening will depend on data. That has taken some of the optimism away from sterling, particularly against the euro, and has led some strategists to say sterling is more sensitive to economic indicators than it has been for most of the past year, when Brexit has dominated price moves.

Others, however, say economic data are still less important than politics, and that it will be difficult for interest rates to be raised before there is more certainty over Britain's departure from the European Union.

Tuesday's numbers showed consumer prices rose by 2.6 percent in June compared with a year earlier, down from a nearly four-year high of 2.9 percent in May.

"Our view on the BoE rate expectations hasn't changed following the data, and we are expecting a rate increase only by end-2018," said Kamal Sharma, senior G10 FX strategist at Bank of America Merrill Lynch in London.

"Since the referendum, the correlation between the pound and the data has broken down, as it is driven more by Brexit headlines," he added.

Sterling, nevertheless, lost more than half a cent in response to the numbers, trading as low as $1.3005 after touching a 10-month high of $1.3126 just half an hour before the data release.

Its move began just before the data was released, re-igniting concern among financial traders that some market players see official economic data before the release time, despite restrictions on access to the numbers.

Against a euro that was trading at 14-month highs against the dollar, sterling skidded as much as 1.2 percent to 88.98 pence per euro, its weakest in six days.

"We have been arguing against a BoE rate hike for a while now, given that inflation has been driven mainly by cost-push factors rather than demand-led," said Piotr Matys, a strategist at Rabobank in London.

"The latest data supports our view that the BoE is likely to refrain from raising interest rates throughout 2018 and perhaps until 2019."