I don't think davidb and I really spent a lot of time in specialist shops until the 32-bit era when we were patrons of Dabhand Computing (run by "the Daves" Atherton and Tomlinson who were also running Dabs Press at the time) in Whitefield, Manchester.
Back in the 8-bit days, having procured an Electron at a Micro User show in Manchester, apart from such annual events it was mostly a matter of going to John Menzies, WH Smith or Boots for games, although you'd find games and other titles in various bookstores (such as
Sherratt & Hughes) and markets in and around Manchester, too. I remember buying Acornsoft products from a stall on the indoor market in the Arndale Centre, Manchester, for instance, and I think even smaller newsagents had small games selections.
There were computer shops, too, and having reminisced with davidb, I think it must have been Micro C in Manchester that had the more unusual machines like the Newbrain (built-in LCD text display!) and probably Atari products. We went on a leaflet/flyer collection spree in our primary school days and undoubtedly got some Atari literature from there. Laskys also had a store in the Arndale Centre, and we tried out the Mac when it first reached the UK in their business centre (which was elsewhere, if I recall correctly).
I seem to remember a computer store in Oldham, on Yorkshire Street perhaps, that did sell Acorn stuff but had mostly given it up when they entertained a few different vendors in some kind of mini-exhibition in the second half of the 1980s, and that's when we managed to buy our Slogger Pegasus disk system direct from the Slogger bloke himself, or so it seemed at the time.
It's remarkable how one often forgets that there were so many people wanting in on the action of the 8-bit era, and how specialist stores, despite ending up pushing the same beige boxes to business customers, started out offering exotic products from lots of manufacturers in what was undoubtedly a very exciting time when nobody knew what would sell and eventually become popular.