The RAC said the higher prices were due to a combination of rising crude oil prices, and the devaluation of the pound after June's Brexit vote.
Average petrol prices rose by 4.4p to 116.7p per litre and average diesel prices rose 5.2p to 118.7p per litre.
The motoring body said these were the biggest monthly increases for three and a half years.
Its fuel spokesman, Simon Williams, said retailers had "no choice" but to put up prices on garage forecourts.
"The effects of the weak pound have really been felt on the wholesale market, and this, combined with an oil price at nearly double its lowest level in 2016, has put significant upward pressure on wholesale fuel prices," he said.
"Certainly, we are a long way from the remarkably low fuel prices enjoyed by families and businesses early in 2016, when the average price of unleaded was around 102p per litre and diesel was 101p," he added.
According to the RAC, the increases mean it now costs Â£64.20 to fill the 55-litre petrol tank of a typical family car.
Meanwhile it costs Â£65.25 to fill up a similarly sized tank in a diesel car.
The RAC suggested that the price of fuel might stabilise in the coming months.
"Opec, which represents some of the world's biggest oil producers, recently agreed in principle a cut in production," said Mr Williams.
"But a final deal is still to be agreed at an Opec meeting at the end of this month and, with some analysts suggesting a deal might yet stall, this leaves open the prospect oil prices might stabilise or even fall before the end of the year," he added.

Operation Anagram was formed by Strathclyde Police in 2006 after Tobin raped and murdered 23-year-old Polish student Angelika Kluk in Glasgow.
It also helped convict him of the murders of 18-year-old Dinah McNicol and 15-year-old Vicky Hamilton.
Police said that while the operation was being scaled back it would never end.
Det Sup David Swindle, who formed the operation, said anyone with information regarding Peter Tobin would still be able to contact the Anagram incident room via e-mail which would be monitored daily.
"Since Operation Anagram was formed in 2006, I could never have believed the momentum and magnitude it would have developed into," he said.
"The public response and assistance from the media has been unbelievable.
"The long-running investigation has brought some solace to the families of Vicky Hamilton and Dinah McNicol in knowing what happened to their loved ones."
Det Sup Swindle said that although Anagram had not uncovered other murder victims of Tobin to date, he was "proud" of its "success in bringing closure" to some bereaved families.
He added: "I leave Strathclyde Police after 34 years in the knowledge that we have tried our best to find out the truth of what Tobin has done and also with confidence that the Anagram processes built up over the last four and a half years ensures a life long awareness of this cowardly, vicious serial killer Tobin.
"Any new information coming to light will continue to be researched which may bring similar closure to other families.
"The search for the truth about what Peter Tobin has done will continue."
Tobin is serving three life sentences for the murders of Vicky Hamilton, Dinah McNicol and Angelika Kluk.
Ms Kluk was raped and murdered at a church in Glasgow in 2006.
The bodies of Ms McNicol, from Essex, and Ms Hamilton, from Redding in Falkirk, were found the following year in the garden of Tobin's former home in Margate, Kent.
Operation Anagram has helped piece together a timeline of Tobin's movements and relationships over decades in a bid to determine whether he is responsible for other unsolved crimes.
Petrol and diesel prices rose sharply in October, said the RAC, taking them to their highest level since July 2015.
[NEXT_CONCEPT]
A dedicated police operation set up to examine the activities of serial killer Peter Tobin is to be wound down.