Before the referendum result, the AA said the uncertainty on voting intentions had meant a dip in the value of sterling.
This, in turn, had led to a slight rise in the price of petrol and diesel for UK consumers despite a fall in world oil prices.
But with the pound already rising following the referendum, the AA is now confident of better fuel deals for UK motorists.
AA president Edmund King said: "We saw early this morning that Scotland's support for staying in the Union boosted the pound.
"The pound rose against the dollar to more than 1.65 at one point which is up nearly one percentage point since midnight. If the pound remains strong we should see reductions in pump prices.
"We believe that if the pound stabilises at these higher levels we should be seeing at least a 2p-per-litre reduction in pump prices which will be great news for everyone north and south of the border."
The AA had earlier said that pre-referendum uncertainty had led to petrol going up from an average of 128.72p a litre on August 31 to 129.23p a litre in mid-September.
Diesel, too, had risen, with the average cost going up from 133.02p a litre on August 31 to an average of 133.44p a litre in mid-September.
The AA said that had the pound held its mid-August value, the average cost of petrol would have now been around 127.5p a litre - the lowest since January 5 2011.
At present East Anglia has the most expensive in the UK, averaging 129.7p a litre. The cheapest is to be had in London and in Yorkshire and Humberside (both 128.9p a litre).
East Anglia motorists are also enduring the highest average price for diesel, at 134.0p a litre, while north west England and Yorkshire and Humberside drivers have the cheapest, both averaging 133.0p a litre.
