joevsw0rld, what Britons refer to as "charity shops", you will know them as they are referred to in the States; thrift stores. In general, the inhabitants of the UK prize music more than us Americans, in my opinion. And thusly, their thrift stores are much better than ours when it comes to finding second hand vinyl. Unless you want Fleetwood Mac's "Tusk" on lp, or a cassette of Warrant's "Cherry Pie", it isn't much use going to a US thrift store in search of music.
I'd suggest bidding on those poor souls who put up lot auctions; multiple items in one auction. Oftentimes I see people selling all the stock UK 7" singles in one auction, all the stock UK 12" singles in 1 auction, etc.
Try to skip the mistakes that every beginning collector makes. Like buying interview picture discs (or really any interview in general), the "Live Panic!" bootleg cd, and not paying attention to the condition of the item when buying it. Every novice collector will have that Red Door or Baktabak interview disc, the hammered "Boy With Thorn" US 12", and the "Live Panic!" bootleg which was recorded at the wrong speed.
You say you're not looking for rarities, but I bet if you quizzed the 100 biggest collectors and ask them, the consensus would probably be that they wish they hadn't bought all the plain jane mundane stuff, and only went for the jugular; the top rarities.
I look back 15 years to when I first started collecting. You could still find the UK Rough Trade cd singles at Tower, and the local downtown record store had many of the German colored vinyl 12"s new for $10, and had several copies of "Education In Reverse" new for $18.
