Diesel prices have risen by the highest month-on-month increase this century.
Meanwhile, rises in the cost of petrol are the second highest since the start of the millennium.
Between mid-April and mid-May, the price of diesel shot up 6.76 pence per litre, from 117.41 to 124.17 pence per litre.
This has added £3.38 to the cost of filling a typical 50-litre fuel tank.
The previous record rise, of 5.6p per litre, was between October and November last year.
The average price of petrol has also risen significantly 4.49p per litre in the past month, from 108.06 to 112.55p per litre.
This narrowly misses the 4.6p record monthly increase in petrol prices between March and April 2006, according to the AA.
A significant gap has opened up between what supermarkets charge for fuel and the price at non-supermarket outlets.
Comparing average prices by brand, supermarkets are 2.5p cheaper for petrol and more than four pence less expensive for diesel.
London remains the most expensive region to buy petrol, while Yorkshire and Humberside remain the cheapest.
“The price rises in recent days were of a magnitude only exceeded in the aftermath of Hurricane Katrina, when the price of petrol rose almost 3.5p in a week,” said Edmund King, AA president.
“What alarms us most is the stream of comments coming from the industry and producers saying that oil is over-priced – the finger of blame being pointed at market speculators.
"Oil prices have doubled since last year and this is not just due to strong demand from China and other nations.
"While huge profits are made in the financial centres, an increasing number of car-owners are becoming desperate and businesses suffer from the hit on consumer spending.”