A number of Asda stores are now listed on the company's website with the number 0844 894 1234. The geographical telephone numbers for those branches now answer with recordings giving the 0844 number.
It appears that Asda is gradually bringing in a centralised number.
Of those stores I've just verified, they all have a sequence of numbers where the old main number with the redirector message ends 00. Each branch has another menu that ends 55 or 15 which can be used to access the store.
From what I can gather, according to listings on
BT Phonebook, in general, stores have similar numbering where pharmacies end 10 and opticians are 12.