MrTFWitt is correct. The fuel is BS compliant and is the same in it's refined state regardless of the 'retailer'. Each retailer be it BP, Jet, Texaco or Tesco add their own additives, that's what makes the difference to the fuel we buy and it's why they can claim one fuel is better than another or we can claim someones elses is rubbish.
The tankers that supply the forecourts all get their fuel from their 'local' distribution depot (remember bunsfield?) and the two main UK refiners for UK distribution are BP & Esso, that's why they make so much money, they are getting a slice from every brand of fuel sold.
Distribution comes down to costs and BP in particular supply the WHOLE of Scotlands fuel, regardless of who sells it. Why would a Jet garage in Aberdeen bring a tanker up from the UK when it can get it on the doorstep, it's the cheaper option. Likeswise why would BP send a tanker from Scotland down to Watford when it can buy it from ESSO on it's doorstep ?
Buying fuel from a different retailer other than BP or Esso does not effect consumption and therefore does not effect the volume of fuel both BP and Esso sell, wholesale.
Now here's a thought... Esso pump fuel up from Southampton to Hemel Hempstead via a network of underground pipes. It's then distributed locally to which ever retailer needs it. Why on earth can't the water companies do the same? The fuel distribution network works, everyone gets fuel and we 'never' run out, they buy and sell and distribute amongst themselves. It's not as if the water companies haven't got the cash !