The September CPI rate was the highest since November 2014, when it was also 1%.
Analysts had expected a smaller increase to 0.8%.
The main upward contributors to the increase were rising prices for clothing and overnight hotel stays but also the plummeting pound which has pushed up fuel prices.
These upward pressures were partially offset by a fall in air fares and food prices.
Tom Stevenson of Fidelity International said: “Even though 1% is still some way off the Bank of England’s 2% inflation target, the impact of currency changes works with a lag so further rises in CPI should be expected.
“Indeed, inflation is expected to continue its upward charge, with some economists predicting that CPI could reach as much as 3% by next year, considerably overshooting the Bank of England’s target.”
This would be bad news for savers who are losing money in real terms.
“To stand any chance of generating an inflation-adjusted real return they’ll need to look further up the risk spectrum, investing in bonds issued by companies rather than the government or moving into stocks and shares,” said Stevenson.