UPDATE 1-UK factory gate prices fall at fastest in 7-1/2 yrs

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LONDON, July 10 (Reuters) - British factory costs fell in June at their sharpest annual rate since 1997 and output prices dropped at their fastest in 7-1/2 years, in a sign inflation will fall sharply in the coming months.

The Office for National Statistics said output prices fell 1.2 percent year-on-year, the sharpest drop since December 2001 and more than the 0.8 percent fall expected by analysts.

Input prices fell 11 percent on the year, less than forecasts for a 12.2 percent decline but still the weakest annual rate since April 1997.

But crude oil prices jumped 14.3 percent in June alone, the biggest monthly rise since January 2005.

"My sense is that given the increase in crude oil prices, input prices will climb again," said Amit Kara, economist at UBS. "Output prices will stay under pressure in the immediate future because of the economic slowdown."

Inflation went up sharply last year because of record high energy prices but policymakers are expecting it to come down just as swiftly in the coming months as Britain battles its deepest downturn in decades. (Editing by Mike Peacock)