UK inflation surprises with slowdown, easing pressure on Bank of England

* CPI slows to +2.6 pct in June vs +2.9 pct in May

* First (Other OTC: FSTC - news) fall in CPI since October

* Factory gate price growth eases too

* Pound falls as investors see less rate pressure on BoE (Shenzhen: 000725.SZ - news) (Adds comments from Carney)

By William Schomberg and David Milliken

LONDON, July 18 (Reuters) - British inflation unexpectedly slowed last month for the first time since October, dousing expectations among investors that the Bank of England might soon raise interest rates for the first time in a decade.

Consumer prices rose by 2.6 percent compared with a year earlier, the Office for National Statistics said, down from a nearly four-year high of 2.9 percent in May.

Economists had expected the rate to remain unchanged and some of them trimmed their forecasts for price growth to just below 3 percent in 2017 as a whole after Tuesday's figures.

But BoE Governor Mark Carney said the "big picture" for inflation remained the same and the main driver was still the fall in sterling since last year's Brexit vote.

"That's what's pushing inflation up, and inflation will be above target for a period of time and today's figures are consistent with that," he told Sky News.

Sterling lost half a cent against the U.S. dollar and British government bond prices jumped as the figures suggested the BoE was under little pressure to raise rates when it next meets in early August, despite concerns among some of its policymakers about rising prices.

The fall in inflation was the sharpest between any two months since February 2015, reflecting a fall in global oil prices, and slowing price pressure in factories.

"This is going to kill the chances of a rate rise in the short term. We will learn more about the Bank of England's thinking in a couple of weeks, but we can expect the calls for a rate rise to reduce to a whimper," Lucy O'Carroll, chief economist at fund managers Aberdeen Asset Management (Frankfurt: 899502 - news) , said.

However, many economists have said they expect inflation to pick up again soon, adding to the strain on households which are seeing salaries rise more slowly than prices.

"There's lots of pressure still in the tank," Alan Clarke, an economist at Scotiabank, said.

Britain's inflation rate has risen sharply since last year's referendum decision to leave the European Union which pushed down the value of the pound, making imports more expensive.

BOE LIKELY TO REMAIN PATIENT

The BoE has been taken by surprise by the speed of the increase this year. Its most recent forecasts saw inflation peaking at 2.8 percent later in 2017 while most economists have said they expect inflation to reach at least 3 percent.

The BoE did accurately predict that inflation in June would be 2.6 percent.

The BoE has so far chosen not to respond by raising rates, saying the Brexit hit to the pound is likely to be temporary.

However, three of the eight BoE rate setters voted to raise rates in June. One of the dissenters has since left.

Carney has said a rate hike would probably be needed if the economy overcomes its slowdown of earlier this year and wages - which are lagging behind inflation - grow more strongly.

The BoE announces its next decision on rates on Aug. 3.

A Reuters poll of economists showed the BoE was expected to keep rates on hold throughout 2017 and 2018.

The ONS said inflation was pushed down by fuel prices after a fall in global oil prices and a partial recovery in the value of the pound last month. A drop in the cost of computer games and equipment, which rose in May, was also a factor.

Data on factory gate prices suggested that the most intense pressure on consumer prices is easing. Output prices rose at their slowest rate since December of last year, up 3.3 percent.

Prices paid by factories for materials and energy rose at their slowest rate since September, up 9.9 percent on the year. (Writing by William Schomberg; editing by Susan Thomas)