Space 1999's debt to 2001 A Space Odyssey is obvious from its very title; both attempted to portray the near future, as mankind begins to explore space.
The opening shots of the film and the first episode are strikingly similar: the Moon moves in foreground, with the Earth and sun seen beyond.
In 2001, a space shuttle is taking a single passenger to the Moon. The stewardess retrieves a pen as he sleeps. In 1999, another shuttle is similarly empty apart from a lone passenger, who accepts coffee from the stewardess. Note the similarity of the black seats and curved bulkheads.
The dark, eerie scenes in Nuclear Waste Disposal Area 2 strongly recall the excavation scenes in Tycho from 2001. One area where Space 1999 was more realistic was having the actors walk with a bounce as if in low gravity; in 2001 the astronauts walk normally.
Keith Wilson's spacesuit design is clearly derived from the 2001 spacesuits.