Ok, I have recently arrived on the as forum as a result of changing cars and have had the 'supermarket petrol' debate on several occasions so here is my take on the subject. Some people will agree and some people will disagree, I don't really care if you disagree, we are all entitled to an opinion but in making the comments I am only trying to help the original poster and having worked in the petrochemical industry both with additive companies and major oil companies in R&D and marketing and have seen the evidence of what I am about to state....... (And I am not trying to be rude about those who disagree, it's just sometimes the debate runs on endlessly and I have had people telling me I have no idea what I am talking about which is fine given I have 25 years experience in the oil industry, if you don't like what I am saying you don't have to pay any note to it)
So...... All fuels are a combination of a base fuel whether petrol or diesel and an additive package. In principle it is the additive package that makes the difference in performance. Most base fuels are the same or similar, the difference is in the premium fuels where they are more highly distilled or refined e.g. V Power / Ultimate etc.
All fuels meet a British Standard, on the face of it fuel is a commodity and any fuel will cause your car to run as designed and more often than not you won't be able to tell any immediate differences. BUT, all fuels are not the same, a lot is said about power outputs and the higher RON fuels can make a difference in highly rated engines (but not so much in every day engines such as those in the Cx5) but in most cases the key element as has been alluded to above is DETERGENCY, in other words how cleanly the fuel burns in your engine and whether it leaves combustion deposits on things such as valves, pistons etc. this is impacted by the additive packages used which tend to be proprietary to each brand.
The oil tankers from the different brands whethe oil co or supermarket will roll up at the local regional refinery and fill with the same base fuel but which will be dosed with the particular brand of additive used by that company.
It follows that those fuels with higher DETERGENCY will keep your engine cleaner over time and hence it will run more efficiently and likely provide better economy but the key phrase here is "over time". Differences are not immediately or always apparent. However you are more likely to pass your MoT if you have been feeding your car branded fuel rather than supermarket fuel, that's not to say cars on supermarket fuels will fail an MoT on emissions, most won't but some will and its more likely with supermarket fuel.
I have seen test rigs that have run engines for thousands of hours on the different fuels and have seen the difference with my own eyes such that I use supermarket fuels in emergencies only. Having spent thousands of pounds on my car I am not going to save a few pennies each time I fill up by using a cheaper fuel.
And finally, for now, a non technical Q&A which might help the doubters.

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Just answer yes/no to the following questions and reach your own conclusions....
1) do you accept that the oil companies spend vast amounts on research and testing of their fuels over millions of miles?
2) do you believe that the supermarkets do the same?
3) do you think that the oil companies would sell their proprietary technology to the supermarkets so that they can undercut them at the pumps.
Now, as they say, go figure.
If you choose to use supermarket fuels that's fine with me, you pays your money and you takes your choice as they say, as I said at the start I am just trying to provide some guidance to the original question and hope this has been helpful.