The cetane improving (and other) additives are, apparently, added at the diesel fuel distribution depot where the delivery tankers are filled - and it this operation which differentiates one 'brand' and type from another. Tankers from numerous fuel 'brand' companies fill their tankers at the same depots.
The larger depots themselves are - like major airports and Defence establishments - linked into a "national grid for fuel", operated on behalf of the government by a semi-privatised company. See
https://en.wikipedia.org/wiki/CLH_Pipeline_System for details.
At an airport connected to the grid, airline operators have their planes refuelled (by contracted pumpers) from tap-off points at each apron. Individual airlines have fuel contract arrangements with individual oil companies (BP, Shell...) but they all draw the same fuel from the same pipe network. Who bills whom is simply a matter of subsequent accountancy; the fuel is all the same. The various oil companies' refineries simply pump their products into the same fuel grid, where, of course, it all mixes.
The major tanker refuelling depots need to be supplied, and, like airports, this isn't done by road tanker! It's a pipeline job (for logistical, security and safety reasons), and the individual oil companies do not, generally, have individual pipelines.
Tesco might well buy its fuel from Esso this month, but the supermarkets exert downward pressure on their buying-in price by shopping around, and so fuel type will not be consistent. In turn, the oil companies and wholesalers trim the price by economising on fuel additives, and one of the casualties of this process is a reduced level of additives (cetane improvers, lubricants, cleaning agents, anti-corrosion, biocides...) in supermarket- and budget-branded diesel road fuel.
Plenty on the web about this:
https://en.wikipedia.org/wiki/Cetane_number
https://en.wikipedia.org/wiki/Cetane_Improver
http://www.millersoils.co.uk/automotive ... sector=Car
-see also the MSDS sheet for what's in it
The differences in "pulling power" will vary from one car to another, and for some vehicles/drivers the differences may not be noticeable. From personal experience, though, all the diesels I've driven run better on good rather than budget fuel. Benefits include better starting, quieter running (down to the action of the combustion-modifying cetane improvers), smoother and better power delivery, and better fuel consumption.
Cheap fuel can often 'pepped-up' by the addition of a good diesel fuel supplement like Millers or Wynn's, to provide what is there by default on best brands. Trouble is, you have to add it, and some of the cost-saving disappears.
I have tried premium-grade ("posh") diesel from several companies, and cannot detect any difference whatsoever between these and their regular stuff. I think it's a marketing opportunity, which most cars don't need, but some drivers think is a good idea.