I'm not sure whether Mieville's Un Lun Dun counts or not; it's a plot point that the protagonist doesn't have magical powers, but the action is mainly set in Un-London, not in "normal" London.

Ah- Sarah Rees Brennan's Demon series- the protag of the first definitely doesn't count, but Mae is one of the POV characters in Demon's Covenant, and she's ordinary. I think Frances Hardinge's Verdigris Deep (Well Witched in the US) qualifies- I think the protagonists are ordinary kids caught up into a witch's snares- and maybe Maureen Johnson's Devilish? I don't remember that one as well.

ETA: Peter Beagle's Tamsin was published in the nineties, wasn't it? It's mostly set on a farm rather than in a city though...