A lot of the time value stuff is the same as the branded stuff. For instance a big chain like Morrisons will go to Mcvities and say will you make us some digestives and put a Morrisons label on please. Think of all the home brands say a chain like Morrisons has. Things like tinned tomotoes, tom purree, cereals, flour, pasta, sugar etc. Morrisons does not have it's own factories producing these items. They pay existing manufacturers to do it for them. I only know this because my Mum worked in a biscuit factory for a few years. My mum also said there was no difference in the ingredients used and the only difference was the label that got put on.
The only company I know of that says it does not make products for anyone else is Kellogs.