The Time Travelers(1964)
A time travel experiment that was supposed to produce a window into time turns out to be a portal instead. One of the experimenters steps through into a not-too-distant-future world that has been destroyed by nuclear war. Some of the others follow, but then the portal phases out and they can't get back. Things just get worse after that. They run across a rocket that has landed to escape pursuing enemies, bearing scientists who survived the war, and many android "slaves." The time travellers are invited to escape when the ship is again ready to blast off - but just before that happens, the scientits' enemy returns and fires on the sitting-duck ship. A very bad day for the scientists turns terminal at that point, and the 20th-century Earthlings barely escape with their skins.