The RAC claimed there is scope for a reduction in pump prices because the cost of a barrel of oil has plummeted to 61 US dollars - the lowest price since mid-November last year.
It warned that a fuel price cut of up to 2p per litre by supermarkets last week only reduced their UK average by 1p because of regional pricing models.
The firm's fuel spokesman, Simon Williams, said: "In order to be fair to motorists the big four supermarket fuel retailers should really make further cuts as the wholesale price is still falling.
"We hope they are not resting on their laurels, thinking they've done enough to keep motorists quiet by announcing some cuts last week when the wholesale price continues to go lower and lower."
Average prices across all UK forecourts stand at Â£1.22 for unleaded and Â£1.24 for diesel.
Mr Williams said the policy of some supermarkets not to offer the same prices to motorists wherever they are in the country means many other retailers do not have to respond to cuts.
He added: "We believe this is why the UK average fuel price hasn't gone down as much as it really should have."
He urged all fuel retailers to reduce their prices, although he accepted this would be harder for smaller operators which deal with lower volumes.