The RAC reported that the average price of petrol had risen from 135.87p on Friday to 136.59p on Sunday, hitting levels last seen in September 2013.
Some drivers claimed to have seen prices jump by as much as 10p per litre.
Filling stations in some parts of the country have been overwhelmed by drivers rushing to fill up amid fears of petrol and diesel shortages, caused by supply issues.
The RAC also warned that further increases could be imminent as retailers pass on the cost of rising wholesale prices to consumers. Wholesale petrol prices rose by almost 2p per litre between Monday 20 September and Friday 24.
RAC fuel spokesman Simon Williams said: “When it comes to pump prices, it’s a pretty bleak picture for drivers.
“With the cost of oil rising and now near a three-year high, wholesale prices are being forced up which means retailers are paying more than they were just a few days ago for the same amount of fuel.
“This has led to the price of a litre of unleaded already going up by a penny since Friday.
“We might yet see higher forecourt prices in the coming days, irrespective of the current supply problems.
“We are also aware of a small number of retailers taking advantage of the current delivery situation by hiking prices, so we’d remind drivers to always compare the price they’re being asked to pay with the current UK averages which are 136.69p for petrol and 138.58p for diesel.”
Comedian Paul Chuckle was among the drivers taking to social media to warn of filling stations that had ramped up their prices. He said he had been charged 14p per litre more than the advertised cost at a filling station on the A1, with other users replying to say they had seen similar increases.
Banking giant HSBC said that its transaction records suggested demand at filling stations was beginning to ease.
Its data showed 25% more transactions over the weekend than compared with a week earlier, with a two-thirds increase in the value of transactions.
However, it said that the number and value of transactions had reduced each day between Friday, 24 September and Sunday 26.
On Friday, the average petrol station was just over £30, compared with just over £20 on a normal Friday.