Petrol prices could dip another 3p over the next two to three weeks, the AA said.
Supermarket cuts have already helped push the average price of petrol to 136.89p a litre.
This is 3.02p lower than a month ago, with average diesel prices having fallen 4.62p to a current 141.76p a litre.
With wholesale fuel prices falling, the AA says average petrol prices could fall to about 134p a litre soon.
At present, the cheapest petrol in the UK is in London at 136.1p a litre on average, while the most expensive is in Northern Ireland (137.8p a litre).
Northern Ireland also has the dearest diesel (142.8p a litre), while Yorkshire and Humberside has the cheapest (140.8p).
AA president Edmund King said: "Last April UK petrol consumption fell. In October it did the same. And in February the UK sold the lowest volume of petrol in 23 years of recording.
"In the past 12 months, oil and fuel price speculation has swung back and forth through the fuel market like a wrecking ball, smashing family budgets, pulverising fuel demand and rocking the foundations of fuel retailer and other business viability."
He went on: "The last 12 months have shown pump price volatility is more acute than ever, driven largely by speculation.
"At least, though, the current prices are going in the right direction - giving drivers a breath of optimistic spring air."