Possivelmente The Doorkeepers por Graham Masterson?
Ocorre em Londres, várias das críticas da Goodreads mencionam realidades alternativas e snippets do Google Livros mostrar resultados para "tuberculosis" e "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."
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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?