Quality Comics was right next door to the Marquis of Granby at 3 Lewisham Way, and seems to have originally been opened in 1975 as Weird Fantasy by Frank Dobson. The rooms upstairs were sublet to Dez Skinn as the base for his emerging comics publishing empire. As Dez recalls, from 1979 he also acquired the shop, renaming it Quality Comics (photos above are from Dez's site).
It was in this period that his Quality Communications launched Warrior magazine as a kind of home grown UK version of a Marvel comic. The 26 issues published between 1982 and 1985 were very influential, featuring among other things the first episodes of Alan Moore and David Lloyd's V for Vendetta
Quality Communications also published the Halls of Horror series from its New Cross office. Not sure how long the New Cross shop/office continued - last Lewisham Way address I have found online for Quality Communications Ltd is from 1984.
Anybody know any more or remember the shop?
Update January 2013 - I came across this advert for Quality Comics 'home of Warrior' today in a 1988 issue of the comics magaazine Speakeasy, so clearly the shop was still going then.