And the extension of the districts in which drivers get a special rural area fuel rebate has failed to kickstart sales at the pumps in some places, the AA said.
The average price of petrol nationwide is now 117.19p a litre - up from 116.42p a month ago and above 117p for the first time since mid-December 2014.
Diesel is now averaging 121.0p a litre compared with 120.7p in mid-May.
Since the low point for fuel prices was reached on February 1 this year, average prices have risen by more than 10p a litre.
Compare fuel prices where you live at petrolprices.com.
An AA/Populus survey showed that 37% of the 28,080 AA members polled had already started to cut back on car use, with this figure rising to 48% for lower-income drivers.
The rural fuel rebate scheme, previously only available for those living on some of the UK’s islands, was extended on May 31 to around 125,000 people living in remote mainland locations, with those eligible getting a 5p cut in pump prices.
AA president Edmund King said: “Our fuel report this month illustrates vividly the power of pump prices on consumer spending.
“It sends out a clear message to government on fuel tax: don’t be mistaken into thinking that because pump prices are 13p-a-litre lower than this time last year that drivers are ripe for another fuel duty increase. “
A Treasury spokeswoman said: “By the end of 2015/16, fuel duty will have been frozen for five years - the longest duty freeze in over two decades. The Government’s action on fuel duty is saving families around £10 every time they fill up their car.
“In addition, the Government’s rural fuel rebate scheme is helping those in the UK’s most rural communities, who face some of the highest fuel prices in the country, to benefit from cheaper fuel.”
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