The Office for National Statistics (ONS) said the Consumer Price Index (CPI) measure of inflation was 0.9% in October, down from 1% in September.
Economists' had been pencilling in a higher figure of 1.1%.
The ONS said there was "no clear evidence" that the plunge in the value of pound since the EU referendum result was bumping up shop prices.
But there were signs that the currency fall was ramping up costs for manufacturers, with the Producer Prices Index (PPI) showing total input prices rising 12.2% in October, compared to a 7.3% rise in September.
The pound's weakness also helped push up output prices to 2.1% last month from 1.3% in September, the ONS said.
It comes as the latest PMI report for the manufacturing industry showed sterling's near 20% slump against the US dollar and 15% fall against the euro since the Brexit vote had triggered the steepest rise in purchasing costs in the survey's 25-year history.
Mike Prestwood, ONS head of inflation, said: "After initially pushing up the prices of raw materials, the recent fall in the value of the pound is now starting to boost the price of goods leaving factories as well.
"However, aside from fuel, there is no clear evidence that these pressures have so far fed through to the prices in shops."
The Retail Prices Index (RPI) - a separate measure of inflation, which includes housing costs- was 2% in October, unchanged from September.
The pound, which was already lower ahead of the data, weakened further as the lower-than-expected CPI figure signalled there would be less pressure on the Bank of England to curb rising inflation.
Sterling fell 0.6% to 1.24 US dollars and 1.1% to 1.15 euros.
The ONS said the biggest downward impact on CPI in October came from clothing and footwear, where the price of garments - especially women's outerwear - rose 0.2% between September and October compared with a 2.3% jump a year earlier.
The cost of education was also dragging down the cost of living, with overall charges climbing 2% across September and October in contrast to a 3.6% rise over the same period in 2015.
The main pressure came from UK and EU student tuition fees, where the impact from the rise in the cap for tuition fees - introduced for new students in England in 2012 - was smaller this year than in 2015 because nearly all students are paying the higher rate.
Food and non-alcoholic beverages made a small downward impact, with non-alcoholic drinks dropping 3.2% between September and October after coming in unchanged over the same two months a year ago. However, food prices fell less than they did a year ago.
The largest upward pressure on prices came from motor fuels, which climbed 2.3% between September and October.
The price of petrol rose 2.6 pence a litre to 113.8 pence, while the cost of diesel rose 2.7 pence a litre to 116.0 pence.
The ONS said: "Fuel prices tend to reflect movements in oil prices and part of the increase in oil prices in 2016 can be explained by depreciation of sterling against the US dollar."
Bank of England Governor Mark Carney said earlier this month that Britons should expect sharply higher costs as the Bank's latest forecast showed inflation shooting up to 2.7% next year.