The consumer prices index (CPI) measure of inflation rose to 5.2% in September, up from 4.5% in August.
Meanwhile, the retail prices index (RPI), which includes council tax and mortgage payments, has gone up from 5.2% to 5.6%.
Both rates are more than double the Bank of England's target for inflation of 2%.
The Office for National Statistics (ONS) says soaring energy prices is the most significant contributor to the higher inflation rates.
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Housing and household costs have gone up by 3.5% month-on-month, as a result of higher energy bills, rent increases and the cost of maintenance.
Problems for UK households
Kevin Mountford, head of banking at moneysupermarket.com, says high inflation is continuing to cause problems for UK households.
"Energy hikes, the soaring price of petrol and the rising cost of everyday basics such as food, have hit households hard. Many workers also have to deal with pay freezes, meaning their incomes are actually dropping in real terms, it is no surprise many feel like their finances are either at, or rapidly approaching, breaking point," he says.
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Inflation is still having an effect on savings and 93% of savers are worried about its effects on their savings, according to the Post Office.
Basic-rate taxpayers need an account paying at least 6.5% to beat inflation and gain benefit in real terms from their savings, increasing to 8.67% for higher-rate taxpayers.
"Inflation continues to whittle away any hope of a decent return on the nation's savings," says Sylvia Waycot, spokesperson for Moneyfacts.
"Today's news offers absolutely no hope for anyone relying on savings interest to help pay for rising food and fuel bills," she adds.
There are now only five savings accounts that beat inflation for basic-rate taxpayers – and two of these are structured products.
Pressure on Bank of England
The official measure of inflation - CPI - is now at an all-time high and the Bank of England has missed its 2% target for the 22nd consecutive month.
Despite calls for interest rates to rise to combat inflation, the Bank's Monetary Policy Committee kept the base rate at 0.5% for a record 31st consecutive month in October.
Thomas Paterson, chief economist at Gold Made Simple, calls this "an epic failure" and says the Bank of England's credibility is "hanging by a thread".
"Whatever external forces the Bank of England blames for the overshoot, the bottom line is that for all of 2011 it has created more than double the inflation the government has asked it to," Paterson adds.
"And what has been its response to missing its government-mandated inflation target for nearly two years? Its response has been to print more money – and not just a small amount but an expansion of the UK's already bloated balance sheet by almost a third."
Paul Mumford, senior fund manager at Cavendish Asset Management, says investors could benefit from inflation as it carries "a silver lining for equities".
"With inflation now running at over 5%, eroding the capital value of bonds, equities are rendered yet more attractive compared to fixed income assets, which at current are struggling to provide investors with decent income. By contrast, equity dividends are steadily increasing," he adds.