The UK faces a potential £5bn bill for a new satellite navigation system, after Theresa May abandoned efforts to remain part of the EU’s Galileo project after Brexit.

Britain may also lose £1.2bn already invested in the scheme after deciding to set up its own system for military use, according to an announcement made at the G20 summit in Argentina.

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.”

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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.

Cabinet ministers resign over Brexit deal Show all 13 1 /13 Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Esther McVey Britain's Work and Pensions Secretary Esther McVey arrives to attend the weekly meeting of the cabinet at 10 Downing Street in London. - Britain's Work and Pensions Secretary Esther McVey resigned from the cabinet over draft Brexit deal AFP/Getty Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @EstherMcVey1 of the resignation letter addressed to Prime Minister Theresa May from Works and Pensions Secretary Esther McVey. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Ms McVey has resigned, saying the Brexit deal âdoes not honour the result of the referendumâ. See PA story POLITICS Brexit. Photo credit should read: @DominicRaab/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Dominic Raab British Brexit Secretary Dominic Raab give a press conference at the end of the final round of talks in Brexit negotiations at the European Commission in Brussels, Belgium EPA Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @DominicRaab of the resignation letter addressed to Prime Minister Theresa May from Brexit Secretary Dominic Raab. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Mr Raab has resigned, saying he âcannot in good conscience support the terms proposed for our deal with the EUâ. See PA story POLITICS Brexit. Photo credit should read: @DominicRaab/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Rehman Chrishti Vice Chairman of the Conservative Party Rehman Chrishti tendered his resignation letter this afternoon PA Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Anne-Marie Trevelyan Parliamentary private secretary in the Department of Education Anne-Marie Trevelyan resigned stating that she cannot support the deal Cabinet ministers resign over Brexit deal Handout image taken from the Twitter feed of @annietrev of the resignation letter addressed to Prime Minister Theresa May from Anne-Marie Trevelyan, a parliamentary private secretary in the Department for Education. PRESS ASSOCIATION Photo. Issue date: Thursday November 15, 2018. Ms Trevelyan has resigned saying she cannot support the Brexit deal after negotiations âbuilt on the UK trying to appease the EUâ. See PA story POLITICS Brexit. Photo credit should read: @annietrev/PA Wire NOTE TO EDITORS: This handout photo may only be used in for editorial reporting purposes for the contemporaneous illustration of events, things or the people in the image or facts mentioned in the caption. Reuse of the picture may require further permission from the copyright holder. PA Cabinet ministers resign over Brexit deal Sam Gyimah Universities minister Sam Gyimah resigned on November 30, claiming the government's decision to pull out of the EU's Galileo satellite navigation system as a deciding factor PA Cabinet ministers resign over Brexit deal Shailesh Vara Shailesh Vara who has quit as Minister of State for Northern Ireland, saying he cannot support Theresa May's Brexit agreement, which he said "leaves the UK in a halfway house with no time limit on when we will finally be a sovereign nation" PA Cabinet ministers resign over Brexit deal Cabinet ministers resign over Brexit deal Suella Braverman Brexit minister Suella Braverman has resigned, stating “It is not what the British people, or my constituents, voted for in 2016.” Cabinet ministers resign over Brexit deal Ranil Jayawardena Parliamentary private secretary to the ministry of justice Ranil Jayawardena resigned as he could not back the deal "in good conscience"

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.

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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.

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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.