I read this maybe four years ago but I think it was a few years older. People keep blundering to a parallel world, they appear in the same dark alleys scattered around a grey grim city. Like fog bound fifties London.
Once they arrive they are seeked out and arrested by what I think is a secret police force who wear like crow masks. They are interrogated for tech secrets. One of the questioners wants to know why phones they find on hapless incomers don't work.
The protagonist crosses over and makes contact with an underground resistance group who hide and help him. They are very interested in how our society can cure TB as they still die of it.
Their tech was similar to our fifties with phone landlines etc but behind ours on medical issues. Also they had a king in a palace somewhere in the city and I think some kind of coup was being planned
Can't recall any more, maybe five hundred page hardback book
Edit/update: They sometimes muttered about TB and sometimes about Scrofula