I once had the idea to do something like this, though the intention was to pitch it to gas station operators as a way to keep their prices competitive (i.e. alert them when the station down the street drops their prices so that they can too and not lose business to casual price shoppers or, alternatively, when the station down the street raises their prices, so that you can too and not lose revenue needlessly) and learned that there are a couple entities, at least in the US, that have national data here. I couldn't even figure out how to contact one, and when I called the other I was essentially laughed off the phone by someone with a VERY New York accent -- it seems from context that their data is VERY expensive and used by Wall St. types, so the idea of some nobody from flyover country essentially reselling it to mom & pop gas station operators was funny, and out of the question.

Also depends on the size of your fuel tank and how full it already is. The time taken to refuel is (almost) the same regardless, but if you've got a 40l fuel tank vs a 70l one or you're only half-empty then it's going to be less worthwhile.

7p cheaper for 10 minutes works out at about minimum wage if you're buying 30 litres, but with a bigger car you could easily be buying twice that, which works out much better.

Although of course you also need to factor in how much fuel you burn driving to the cheaper place, and the extra wear and depreciation on the car. If you take the HMRC standard rate of 45p/mile (which was meant to cover all of that kind of thing, but hasn't been updated for years) then even going a few miles out of your way quickly ends up costing more than it's likely to save.

mostly such tools are useful when you go very close to a few petrol stations on your regular routes anyway. I can pretty much time topups for when the cheapest station locally is en-route to my destination

A 7p per litre difference does sound like the difference between local station and motorway prices though, and they probably will have factored in that opportunity cost of time...