I can only speak from my own personal experience:
I had a Citroen C3 1.4 HDi 8v, which for most of it's life was run on Tesco diesel, with the occasional tankful from Asda or one of the 'brands' (either Shell or BP). At a rough guess I'd say it was around 80% of the fuel came from Tesco, with the others fairly evenly split over the rest. It never missed a beat in over 100,000 miles.
Then
Morrisons started doing a promotion which made it worth going there to fill up. Within two tankfuls I'd noticed that the tickover was getting increasingly lumpy and the engine was slightly hesitant under load. I didn't put the two together immediately but after a month or so spoke to the garage who look after the car and they checked it over and the first thing they asked afterwards was where I'd bought the fuel from.
When I told him he smiled and recommended that I run a tankful of Shell V Power diesel through it and then switch back to Shell Fuel Saver diesel after that and see how things went.
Before the car had finished that first tank of V Power diesel it was running normally again, and continued to do so until I sold it a couple of years later. Although I'll still buy fuel from other supermarkets I haven't bought Morrisons diesel since.