Nice idea but..............
Esso and BP are seperate companies. You've got Exxon-Mobil who own the Esso brand and also BP Amoco who own the BP brand. The problem is if you don't buy from them directly and use the supermarkets then they'll just buy off them anyway as they're only a finite number of refineries in the UK and hence only a limited amount of fuel to go round.
Also once you boycott BP and Esso, what's to stop the other companies putting up their prices as everyone's going there? It's the standard principle of supply and demand. Rather than just boycotting various fuel suppliers, you should reduce your fuel consumption and hence reduce the overall demand as a whole. One method of doing that is looking at alternative sources of energy. Even LPG isn't the answer as you're still dependant on the oil companies.
If you want lower prices, you're going to have to look why the prices are so high... taxation and demand will be a start. Boycotts will never work as it requires sacrifices on the part of the boycotters which people often are unable and unwilling.
The price of oil per barrel has risen over the past 6 years anyway (dramatically) look at the situations in the middle east (another vein to this is that US oil reserves are runnning out and Iraq has loads of oil - hmmmmmm, why did bush invade <_< - but that's another topic !)
Taxation on fuel will reduce when hell freezes over - the government make far too much money from it. There is currently a deficit every year anyway, if fuel prices drop then expect other taxes to rise.
It's a no win situation.
Sucks but doubtful it will change.