I agree with others that this was a complete non-issue stirred up into a problem by the media and individuals on social media. The media are desperate for stories on the lorry driver shortage (which has been going on for years) and a few days ago 8 petrol stations (out of 8,543) had supply problems due to delayed deliveries. The media jumped on it, inflated the issue, everyone panics and, before we know it, we have shortages all around the country! There was no petrol shortage, but now there will be!
As for queues, it’s not widespread. We are currently on holiday on the Isle of Wight. I filled up in the garage in our village Thursday night the day before we left. Just one car in front of me. Topped up in Asda when we arrived on the Isle of Wight yesterday afternoon. Had to wait no more than 3 or 4 minutes. We’ve driven past numerous petrol stations today (inc 2 different Morrison’s) and no queues at all. Free pumps and no shortages. One of our daughters filled up in Asda at Cribbs Causeway Bristol (a massive one) at 4.30pm yesterday. Barely any queues. Paid at the pump (as I always do) and was fuelled and out in less than 5 minutes. Yet listen to the media and watch the pictures of the stations with long queues and you could be forgiven for thinking it’s like that everywhere.