Supermarkets Asda and Morrisons have reduced their fuel prices by 12p per litre for petrol and 8p per litre for diesel.
The RAC said it is the largest single cut it has seen and predicted it will result in prices sinking to a four-year low.
Oil prices have plunged in the past few weeks since Covid-19 took hold across Europe.
They were also heavily dented when Saudi Arabia, which produces around 10% of the world's oil, decided to slash prices and ramp up production in a trade war with Russia.
The price of a barrel of Brent crude oil, the most used measure, has fallen by around 60% since the beginning of the year.
It slipped another 5.7% to 25.53 US dollars per barrel on Monday.
Latest Government figures show the average price for a litre of fuel at UK forecourts on March 16 was 120.3p for petrol and 124.4p for diesel.
RAC fuel spokesman Simon Williams said: "These unprecedented times are leading to unprecedented price cuts on fuel – the largest single cut from retailers we've ever seen.
"The price of oil has fallen so far – down to an 18-year low – that it was inevitable that pump prices would eventually follow suit."
He added: "These savings will directly benefit those people who continue to rely on their vehicles for essential journeys.
"It is vital, however, that drivers heed Government advice and only travel if it absolutely needed.
"Drivers need to take sensible precautions when filling up – follow the social distancing guidelines and use disposable gloves when handling pumps or indeed electric car charge point nozzles."