When Quentin and Julia first arrive in 1942 London a Black Cab drives across the screen, however it is a Hackney Carriage which would not be in use until the 1970's.
When Quentin & Julia arrive in Fillory, they're 70 years behind their friends. They meet a young Martin Chatwin who takes them to a knife maker whom they commission to create the Leo Blade, a weapon powerful enough to kill the Beast. But the Beast, knowing full well the blade has been created, does not fetch it himself, before Quentin & Julia are whisked forward in time by the Watcherwoman.