Prices of clothing, footwear and recreational and cultural activities have also risen.
However, there is some good news for families as inflation on the price of food has slowed for the first time since March.
In addition, private school fees have risen by less than a year ago, along with pre-owned cars.
Jonathan Loynes, chief European economist at Capital Economics, said: "September's figure will be the peak in inflation and the key issue now is how far it will drop back."
He added that sharp falls in inflation would help families' spending power and allow a cut in interest rates.
The British Retail Consortium has said that retails sales have fallen for the sixth month in a row, with furniture sales the worst-hit.
It added that impulse buying was disappearing and families were opting for value food ranges.
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