The CPI last time was 3% in April 2012, but was driven by higher transport and food prices.
The increase in inflation increases the likelihood of an increase in interest rates next month.
The significance of these increases is that government pension payments from April 2018 will rise in line with the CPI in September.
Business rates will go up by September's Retail Prices Index (RPI) of 3.9%.
The fall in the pound since last year's Brexit vote has helped to push up inflation.
The basic state pension is protected by the "triple lock" guarantee which means it will go up next April by a rate equal to September 2017's CPI, earnings growth or 2.5% whichever is the greatest.
However, Chancellor Philip Hammond could amend that in next month's Budget.
Letter to chancellor
At the moment, the full new state pension is £159.55 per week, equivalent to £8,296.60 per year.
Bank of England, Mark Carney, has narrowly avoided having to write a letter to the chancellor, only necessary if inflation reaches more than 1% either side of the 2% target.
ONS Head of Inflation Mike Prestwood said: "Food prices and a range of transport costs helped to push up inflation in September. These effects were partly offset by clothing prices that rose less strongly than this time last year."
Laith Khalaf, senior analyst at Hargreaves Lansdown, said: "The tick upwards in inflation will increase expectations of a rate rise from the Bank of England later on this year, stoked by a flurry of hawkish rhetoric coming from Threadneedle Street."
However, he added, it is not a foregone conclusion, "so it's probably best not to count those chickens until they're hatched".
Analysis: Brian Milligan, Personal Finance reporter
Pensioners' delight
Pensioners will be celebrating again.
Today's CPI inflation figure means they will get a 3% rise next April, their largest pension increase for six years.
Those on the new state pension will see their weekly income rise to £164.
Compare that to workers, who've seen their earnings rise by 2.1% over the last year.
This is all thanks to the triple lock, which sees the state pension rise by the highest of earnings, prices or 2.5%.
Food for thought for the Chancellor, perhaps, who's reported to be considering tax concessions for younger people in his forthcoming budget, to even up the inter-generational unfairness that the triple lock has contributed to.
The 2.5% element of the triple lock is due to be dropped in 2021.
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