The government is being urged to cut the amount of fuel duty. Independent retailers say they are being crippled by small profit margins.
Queues to buy fuel continue as stations run out across the region.
West Sussex County Council has issued a statement advising motorists how to cut petrol use as the panic buy continues.
The scene in Aylesbury in Buckinghamshire where people are panic buying fuel.
Here's a selection of views from ITV Meridian's Facebook site. There are a lot of people out there queuing for petrol and diesel. But, it seems, all the panic buying is making things worse:
Karlene Heath These motorists need to stop and use their common sense. They are causing the very shortage they are trying to avoid being affected by. If you don't have to fill up right now -DON'T!
Jayne Norman My car is empty, I need fuel to get to a family funeral in the north of England but every place round me is either closed or rationing. I do not expect to sit in the petrol station for an hour with 4 young children getting hotter and hotter in the car.
Panic buying has meant that this petrol station in Thame in Oxfordshire has run out of fuel.
There's heavy traffic on the B3080 Lode Hill in Sailisbury.
Further delays on the A2030 Goldsmith Avenue, westbound, and the A2047 Kingston Road, northbound, in Portsmouth.
And queueing traffic on the A353 King Street and A354 Dorchester Road in Weymouth, all caused by queues at petrol stations.
There's no diesel fuel now available at Fleet Services, northbound on the M3. Petrol is still available, reports say.
Motorists still panic-buying fuel despite no strike being called. Queues to be expected in vicinity of garages. Pls don't queue dangerously.
The panic buying of petrol was continuing this morning as motorists queued for fuel.
This is the scene in Park Gate in Hampshire a short time ago.
Nearby stations have run out of fuel, meaning that this garage had people queuing in a desperate bid to fill up.
Traffic is already queueing for petrol in Portsmouth - back to Sainsbury's from the petrol station on the A3 Commercial Road, northbound to All Saints' Street.
And in Cosham, there are similar reports of queueing traffic on the A397 Northern Road, northbound, from the petrol station to the roundabout
Our political correspondent Phil Hornby analyses the race to stock up on fuel. In this report we hear from residents in Sussex, Chief Inspector Nick Maton from Dorset Police, filling station owner Louise King and shadow chancellor Ed Balls MP.