A row over Galileo, which the bloc is developing to rival the U.S. Global Positioning System, erupted earlier this year when London accused the EU of shutting British businesses out of the project before Britain's exit next March.
The EU has said its rules prohibit it sharing sensitive security information with countries outside the bloc.
Britain will explore options to build its own Global Navigation Satellite System to help guide military drones, run energy networks and provide essential services for civilian smart phones, May's office said. It will also work with the United States to continue accessing its GPS system.
"I have been clear from the outset that the UK will remain firmly committed to Europe's collective security after Brexit," May, who is attending the G20 Summit in Argentina, said in a statement.
"But given the Commission's decision to bar the UK from being fully involved in developing all aspects of Galileo it is only right that we find alternatives."
Britain told the EU earlier this year it would demand the repayment of up to 1 billion pounds ($1.3 billion) if the bloc restricted its access to Galileo.
A senior British official said the question of past contributions was still a "live issue" which would be discussed as part of talks on Britain's future relationship with the bloc.
In August, Britain said its UK Space Agency, with support from the Ministry of Defence, would start work on an alternative satellite system to Galileo to ensure its national security if it were barred from equal access to the EU programme after Brexit, setting aside 92 million pounds for it.
"I cannot let our armed services depend on a system that we cannot be sure of. That would not be in our national interest," May said.
May's office said Britain's Overseas Territories and Crown Dependencies would be used to provide a global network of locations needed for the ground-based infrastructure and worldwide coverage. ($1 = 0.7839 pounds) (Reporting by Kylie MacLellan; Editing by Hugh Lawson)
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