The motoring organisation said a litre of unleaded now costs 167.17p - the biggest weekly increase since April - while diesel has also risen by 5p to 188.63p.
Fuel prices have soared since the US-Israel war with Iran began at the end of February, with the fighting severely disrupting supplies of crude oil - a key ingredient in petrol and diesel - across the Middle East.
The price of Brent crude, the global benchmark for oil, has returned to $100 a barrel, for the first time since July, as hostilities escalated again.
US forces struck five Iranian tankers after Tehran targeted one of its warships, while Yemen's Iran-backed Houthi movement also attacked oil facilities in Saudi Arabia.
The price of Brent is some way off the $120 it hit in April, but remains well above the $70 it was trading at before the conflict started.
