The pilots of light aircraft and sailing boats are believed to be particularly at risk of accidents if the equipment fails.
GPS is a US satellite network which transmits signals to receiving equipment, allowing users to accurately chart their position. It is very widely used by millions of private, commercial and military users.
Amateur sailors could be most at risk
But at midnight next Saturday, the system's time signals will automatically reset themselves to "week zero". Some receiving systems, particularly older ones, may believe the date is 6 January, 1980, and fail. In May, a US inquiry heard that devices over five years old are "probably going to have a problem".
The US Department of Defense, which runs the GPS system, warns that a failing device could present one of the following problems:
It will be unable to locate satellites, resulting in the receiver not working
It will take more time than usual to locate the satellites
It will appear to be working but display inaccurate positions, times or dates
Each of the 24 satellites orbits Earth twice a day
The problem, known as the "end-of-week rollover", comes from the way satellites keep track of time.
They count the number of weeks since their launch at the start of 1980, but only up to a maximum of 1,024 weeks (19 years, eight months). They then return to week zero.
Military, space and most commercial systems are thought to be well prepared. The UK Ministry of Defence has missiles, aeroplanes, ships, submarines and vehicles all using GPS but say all necessary repairs have been carried out: "We will not have any problems."
However, GPS receivers can now be bought for less than £100 and are increasingly being used by small businesses and amateur sailors and walkers. They could be hard hit, as they are less likely to have non-GPS, back-up systems.
Professor Bradford Parkinson, who helped develop GPS, told the BBC that the problem had been understood for a long while and it was unlikely that any commercial flights or sailings would be affected. He thought private users might have some problems but that these were "akin to having the batteries run out".
Conservative Party's transport spokesman, attacked the government for not making more effort to warn the public. It was a "potentially very irresponsible attitude", he said.
The UK's Department of the Environment, Transport and the Regions said GPS was a US system so if "people choose to buy into it, it is their look-out."