I’ve been through this on another channel.
Essentially, “premium” fuel more because it contains more detergents that supermarket fuel; “Ultimate” and “Vpower” etc contain cleaners, and a minute extra power gain through added combustion. Normal premium has less “cleaners” but more “keep it clean” so yes its worth using BP / Shell normal vs supermarket fuel which is relatively dirty. Note that an already clean engine will not perform any better with normal premium fuel.
The advice above is correct. The DPF will either passively (by getting heated up during normal driving) or forcibly (the ECU forces fuel to be burned at high temps – known as a regen process) burn off soot to keep the DPF from being clogged. Most modern cars don’t do this (esp. the forced region) until a certain few conditions have been met; The engine must be at optimum temp, the car is driving circa/over 2000 revs. This process normally takes about 10 minutes and in most modern cars is imperceptible. You may feel a loss of power, reluctant accelerations, smell of burning if stationary, lower current MPG, or puff of dirty smoke during acceleration.
The most likely time for this to happen is on a typically motorway journey. Short stop start journeys do not meet the conditions and therefore you will be building up soot throughout the system. So to look after you engine spend a few extra pence on a branded fuel, and take it for a long journey to invoke the DPF regen. Your dealer can forcibly invoke the regen on the ramp via the ECU if necessary.