By David Milliken and Alistair Smout LONDON (Reuters) - British consumer price inflation unexpectedly held steady last month, bucking market expectations for a renewed rise, after fuel prices fell and the effect of the pound's tumble after last year's Brexit vote started to fade. Inflation is still likely to edge higher, further squeezing living standards and consumer spending, and the Bank of England predicts it will hit a five-year high of about 3 percent around October. But after more than quadrupling since Britain voted to leave the European Union in June 2016, there are now signs that this surge in inflation is beginning to level off. Consumer price inflation held at 2.6 percent year-on-year in July, unchanged from June and below the near four-year high of 2.9 percent struck in May, the Office for National Statistics (ONS) said on Tuesday. Lower petrol prices in July were offset by higher costs for food, clothing and household goods, it said. Economists polled by Reuters had on average forecast a rise to 2.7 percent in July, and sterling fell to a five-week low against the U.S. dollar after the data, as traders saw little chance of the BoE raising interest rates soon. "Most of the currency-related inflation bump is behind us," Barclays economist Fabio Fois wrote in a note to clients. "Overall, goods inflation has been underwhelming and the sharp drop in producers' input prices inflation continue to suggest that imported inflation is set to ease from here on." Sterling has fallen 14 percent against a basket of currencies of its main trading partners <=GBP> since last year's Brexit vote, and the biggest impact so far has been on the cost of manufacturers' raw materials. So-called input price inflation reached nearly 20 percent annually in January, its highest since 2008. But Tuesday's data showed this eased to a one-year low of 6.5 percent in July, down from 10.0 percent in June. It was the biggest one-month drop in the rate in more than five years, as year-on-year price comparisons now include the post-referendum period. The prices factories charge for goods rose at the slowest rate since December at 3.2 percent. INFLATION STILL TO PEAK? Nonetheless, further increases in consumer prices are likely as the effects of past price rises spread across the economy. Britain's biggest energy supplier, British Gas , plans to increase electricity prices by 12.5 percent next month. And commuter rail fares will rise next year by 3.6 percent, July's rate of retail price inflation - an older measure that the ONS says is no longer reliable, but which is still widely used in British commercial contracts. Data due on Wednesday is likely to show average pay rises of around 2 percent are failing to keep up with the cost of living. "The squeeze on cash-strapped families continues to grip," Trades Union Congress General Secretary Frances O'Grady said, asking the government to do more to lift pay. After the expected peak in CPI around October, the BoE expects it to stay above its 2 percent target for the next three years, based on its experience of a previous fall in sterling 10 years ago at the start of the financial crisis. But economists doubted Tuesday's figures would encourage any more members of the central bank's rate-setting Monetary Policy Committee to join their two colleagues who favour a rate rise. "The MPC should 'look through' this and keep rates on hold," said HSBC economist Chris Hare. ONS figures on Tuesday also showed a modest slowdown in house price inflation, which edged down to 4.9 percent, its lowest since March's three-year low of 3.9 percent. Prices in London alone grew by 2.9 percent, with similar rises in Scotland and northeastern England. Prices rose most in eastern England. For graphic on UK inflation, click - http://tmsnrt.rs/2uYfurQ (editing by Alister Doyle)