Book, portal to a parallel world, secret police in crow masks rule

Question

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

Answer 1

Possibly The Doorkeepers by Graham Masterson?

It takes place in London, several of the Goodreads reviews mention alternate realities, and Google Books snippets show results for "tuberculosis" and "Hooded Men".

“Well, the Hooded Men want us to believe that it's Purgatory, to discourage us from trying to visit it, and to give them an excuse for capturing and killing everybody who accidentally makes their way through."

and

How could there be another world where people went by train under the Channel and people flew to New York in three hours and there was color television and cures for tuberculosis and almost everybody was connected to >almost everybody else by computer?