Wholesale prices have dropped and motoring organisations have suggested this merits reduced pump prices.
Tesco and Morrisons are cutting prices by 2p a litre on Friday, and Asda and Sainsbury's said they would reduce prices by up to 2p a litre on Saturday.
But drivers are being warned that prices can vary in different areas.
The average UK price for a litre of unleaded petrol was 118.83p on Thursday, and 120.88p for a litre of diesel, according to the latest figures from Experian Catalist.
Ten days earlier, the average unleaded price was 120p a litre, and diesel cost 122.06p.
The oil price and wholesale prices fell sharply at the start of March, and motoring organisations have argued that this should have been feeding through to another 2p cut per litre in prices at the pumps.
The RAC said motorists could feel "aggrieved" that prices had not fallen further, earlier.
Asda said it had dropped prices twice in two weeks, and had a national price cap to ensure motorists were dealt with equitably. Morrisons said it had also made a second cut in two weeks.
Tesco is dropping petrol and diesel prices by 2p a litre over the course of Friday afternoon at all its outlets, followed by Sainsbury's on Saturday.
Luke Bosdet, of the AA, said that there was general concern that so-called supermarket fuel price wars did not actually benefit all drivers across the country.
He claimed prices fell the most in areas where there were a range of supermarkets located close to each other. In other areas with less competition, the same cuts were not as likely to be seen.
"We would urge motorists to look around to find a better price. There are petrol price apps that can help," he said.

Chris Grayling told MPs it wouldn't be "sensible" to spend taxpayers money on translation facilities but said the government might review the ban if a new MP couldn't speak English.
He was responding to a call from his Labour shadow, Chris Bryant, who suggested MPs could be allowed to speak Welsh during meetings of the Welsh grand committee.
Mr Bryant asked him: "I understand that the language of this House is English but Welsh is the mother tongue of many of my compatriots and constituents so is it not time we allowed Welsh in the Welsh grand committee?"
Mr Grayling replied: "I have given this careful thought. In my judgement, given the fact that English is the language of this House and given the fact it would cost taxpayers' money to make a change at this moment in time, if somebody arrives in this House who cannot speak English we may need to look at this issue again but I think we have considered this issue very carefully and we should retain the situation where English is the language of this House."
MPs have been able to speak Welsh when the Welsh grand committee (made up of all MPs from Wales) has met in Wales and the Welsh affairs select committee (made up of 11 elected MPs) has taken evidence in Welsh at Westminster.
Mr Grayling's comments annoyed Cynon Valley Labour MP Ann Clwyd, who told him: "Can I remind you that some of us took the oath in joining this House in both English and Welsh and I'd ask you to look again at the proposal to use Welsh in the Welsh grand committee? Some of us did not speak English until we were aged five and most of us are now bilingual but nevertheless the Welsh language and its status is very important."
He told her: "Of course I do absolutely understand the need to protect the Welsh language and indeed across different administrations over the last generation extensive steps have been taken to protect the Welsh language, to make it very much a part of routine life in Wales.
"My question to you really is: at a time of financial pressure, is it really sensible for us to be spending taxpayers' money in a House where the prime language, the main language, the official language is English, when we have members of this House who are able to talk in that language? As long as that is the case, I have considered it carefully but I don't believe we should change things."
Discuss.
Motorists will see an acceleration in fuel price cuts over the weekend as supermarkets take up to 2p off a litre of petrol and diesel.
[NEXT_CONCEPT]
The leader of the House of Commons has rejected calls from MPs to overturn a ban on speaking Welsh at Westminster.