Usually, there were separate Co-op "companies" in each town or city (mostly in Northern England, I think.), so my late mother's number would apply in her local St. Helens Co-op branches, but not at Co-op shops in Liverpool or elsewhere. I think "divi" must have been abolished when local Co-ops became more integrated into a national structure, possibly in the 1960s or 1970s.
The national structure was really just a wholesale operation owned jointly by the participating local societies until very recently. There were a fair number of mergers leading to larger regional groups over time, but no wholesale disappearance. The local societies spread well into the midlands and Scotland, and I think the Leo's brand was controlled by the southwestern regional society, so presumably they were down there as well. I think the divi numbers were just replaced by stamps because it was easier more than anything else
I worked in the Co-operative Movement for over 25 years, before leaving in 2014. A few points.
A Co-op is a mutual organisation and should be referred to as a Society, never a company!
In the early 20th Century there were more than 2,000 co-operative societies across the UK. Many were single shop Societies based in a town or village
Most Co-operative Societies chose to buy their products and services through the Co-operative Wholesale Society which was a large manufacturing and wholesaling business owned by co-operative societies but generally they were independent businesses free to set their own prices, marketing etc
As competition intensified many co-operative societies merged with neighboring societies and by the 1990s there were around 50 societies remaining. The largest 10 accounted for around 80% of co-operative trade
Co-operative Retail Services was set up to operate co-op stores in areas where there was no co-operative society. Some societies were taken over by CRS where they unable to be rescued by neighbouring societies. CRS operated stores branded as LEOs
The Co-operative Wholesale Society became a retailer in its own right when the took over societies such as Royal Arsenal, South Suburban and Greater Nottingham who had got into financial difficulties but were unable to be rescued by CRS due to their own financial difficulties
CWS and CRS merged in 2000 to create The Co-operative Group. Since 2000 further consolidation has taken place with other large societies being taken over by the Co-operative Group.
A handful of independent societies remain, notably Midcounties, Central England, East of England although there are still some small societies such as Radstock and Tamworth.
Dividend is payment on the profits to the members. Unlike a PLC where it is based on the number of shares held in a co-operative society it is distributed based on the level of purchases which is why it was important to make sure a divi number was given when buying from the co-op. in the 1970s most Societies switched to using Dividend Stamps as a way of paying the dividend as it was more cost effective. Come the 1990s member cards are used in most Societies to record transactions.