Diesel drivers could be even worse off, with pump prices up by as much as 12p a litre by December.
The forecast comes following the price of Brent crude oil increasing by £13 a barrel since the middle of this year, up by about 20 per cent.
It prompted calls for Chancellor Philip Hammond to scrap a fuel duty rise in his Autumn Statement next week.
A barrel of oil is trading at more than $63 (US dollars), the highest since June 2015.
It means a definite price hike at the pumps for Britain’s 37 million drivers, say experts.
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The RAC motoring group predicts petrol will rise by 3p a litre from its current 119p average, while diesel will go up 1p to 121p.
But George Buckley, UK economist at investment bank Nomura, predicts bigger hikes of between 7p and 8p a litre.
Simon Williams, the RAC’s fuel spokesman, said: “Motorists are going to be hit by rising pump prices in the next few weeks.”
If the average car uses about 35 litres of fuel a week, Nomura’s forecasts would add £150 a year extra to motoring bills.
Mr Buckley estimates that petrol prices are set to rise by 6.5 per cent at a time when food prices are going up 3.5 per cent, but earnings are lagging behind at 2.2 per cent.
Howard Cox, of the pressure group Fair Fuel UK, called on chancellor Philip Hammond to freeze fuel duty in his budget on November 22.
Fuel duty has remained at 57.95p a litre since 2011, but diesel is taxed higher than other EU countries.
Mr Cox said: “Britain’s struggling small traders and businesses deserve and need all the help they can get”.
Further rises in petrol and diesel will boost inflation and put pressure on the Bank of England to raise interest rates again, he warned.