This is a recurring myth. First of all, Redex. I had petrol vehicles, before supermarket fuel stations existed. I have poured Redex through the carb., and it always produced an abundance of white smoke, so forget the supermarket fuel connection.
When supermarkets began to supply fuel, I started to buy my petrol from these outlets, and have continued to do so since I changed over to diesel so some 17 years ago. My present VW Touran has consistently run on supermarket City Diesel, mainly from Sainsbury's pumps, is now over eight years old, and there has never been a problem or any reason to suspect any downside.
My previous Touran, now 12 years old and now owned by a family member, has spent much time in France as well as England, has run on supermarket diesel both there and in the UK, and is still running perfectly OK.
Supermarkets can buy their fuels cost effectively because of the collectively massive amounts of fuel they purchase. Also, they can afford to cut prices to attract customers to continue on into their stores which boosts sales. Furthermore, under the sale of goods acts and EU directives, fuel quality has to meet stringent standards.
Still sceptical? Well, at our Fosse Park Sainsbury's, close to M1/M69 junction, police vehicles can regularly be seen to be filling up here. Considering the hard life of these vehicles, and reliability requirements, do you think the police would use supermarket fuel if there were any doubts about its qualities? When I read these spurious tales about supermarket fuels, I simply laugh at them and carry on!