The estimated cost for the UK of building an alternative is £3bn to £5bn, although the government has declined to put a figure on the bill.
The move means the government has rejected the EU’s offer for the armed forces to use Galileo’s secure systems, because the UK will be barred from decisions on its development.
It was attacked by Dominic Grieve, the former Conservative attorney general and supporter of the anti-Brexit Best for Britain group, who told The Independent: “This news will leave most Britons lost.
“Brexit was supposed to increase our strength and influence, yet here we are pulling out of a key project of great importance to our national security. To compound this disaster, we will have to pay out billions to replace the project.”
But Ms May defended the decision, saying: “Given the European Commission’s decision to bar the UK from being fully involved in developing all aspects if Galileo, it is only right that we find alternatives.
“I cannot let the armed forces depend on a system we cannot be sure of. That would not be in our national interest.
“And, as a global player with world-class engineers and steadfast allies around the world we are not short of options.”
The announcement came after the EU piled further pressure over Brexit, by rejecting the prime minister’s surprise suggestion that her deal could be renegotiated, if MPs throw it out.
Donald Tusk, the European council president, said there was no other deal on offer and the only options were to leave with no deal – or to remain in the EU.
“If this deal is rejected in the Commons, we are left with, as was already stressed a few weeks ago by prime minister May, an alternative. No deal or no Brexit at all. I want to reassure you that the EU is prepared for every scenario.”
Meanwhile, the prime minister ducked two chances to say she can still win the crucial vote on her Brexit deal, amid mounting evidence that MPs will reject it on 11 December.
She also came under pressure to push harder for the truth behind the killing of Saudi journalist Jamal Khashoggi, after Emmanuel Macron demanded an international investigation.
Confirming the Galileo pullout, Ms May did not explain which “steadfast allies” would help develop an alternative – but stressed the British system “must be compatible with the US GPS system”.
Australia has previously been suggested as a partner in the project, although Ms May has also insisted the UK has the ability to go it alone.
The latest move is the culmination of one of the bitterest Brexit disputes, after Brussels insisted full participation in Galileo was impossible for any “third country”.
Under EU rules, non-member states cannot be involved in the development of secret technology behind Galileo’s secure public regulated service (PRS), a military-grade signal.
British space companies have been blocked from contracts worth hundreds of millions, despite having been heavily involved in the development of the service.
In the summer, the government announced it was spending almost £100m on an 18-month study to develop the UK’s own version of Galileo – a project that will not go ahead fully.
The UK would be allowed to use PRS with a security agreement, but had insisted it needed oversight of the secure technology and its future development to have confidence in it.
A failure of the service could cost the UK economy £1bn a day, with more than 11 per cent of the country’s GDP directly supported by it.
Dependable navigation and timing services are “increasingly essential for defence, critical national infrastructure and emergency response”, a UK official said.
The government and EU will still negotiate whether the UK can use Galileo for non-military purposes, as part of the future trade talks.
If those talks fail, the UK is likely to push for some reimbursal of its £1.2bn outlay, but with no guarantee of success.
The eventual cost of a replacement is likely to depend on which partners can be persuaded to take part in its development.
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