Petrol prices rose nearly 7p per litre, pushing up the cost of filling a tank by £3.74.
Diesel went up 8p, making filling a tank cost £4.41 more, the motoring organisation said.
But the RAC, representing drivers, said fuel retailers were not increasing the profit they were making.
"August was a big shock to drivers as they had grown used to seeing far lower prices than last summerʼs record highs," said the RACʼs fuel spokesman Simon Williams.
But he said a recent investigation by the competition regulator appeared to be making retailers more cautious about raising prices further than necessary.
"They have clearly been influenced by the Competition and Markets Authorityʼs investigation as, all of a sudden, margins are once again closer to their longer-term averages," Mr Williams said.
A CMA investigation earlier this year found that weak competition meant supermarket margins on fuel had increased, resulting in extra costs for drivers. As a result retailers agreed to set up a scheme to allow motorists to compare live fuel prices online.
Mr Williams said he believed retailers were using Augustʼs rise in the wholesale cost of fuel to "subtly cover their tracks" because reducing prices at the pumps immediately following the competition investigation would have been "far too obvious a step".
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UK pump prices rose steeply during 2021 and the first half of 2022, driven by Russiaʼs invasion of Ukraine. Prices fell back in late 2022 and the first half of this year, before this recent uptick.
Earlier this year Opec+, the group of oil-producing nations which meets regularly to determine whether to increase or decrease production, agreed to reduce supply. As a result the oil price has risen by nearly $12 a barrel to nearly $87.
The average price of unleaded petrol was 152.25p at the end of August. A litre of diesel cost 154.37p.
The RAC said the petrol price rise was the fifth largest monthly rise for 23 years, exceeded by a steep rise in October 2021 as the global economy reopened after the pandemic and three sharp monthly rises in early 2022 after Russia invaded Ukraine.
Dieselʼs monthly rise was the sixth largest in the past 23 years.