David Davis has accused the EU of "shooting itself in the foot to see if the gun works" by weakening security ties with the UK after Brexit.
In a speech in London, the Brexit secretary criticised the European Commission for putting legal precedents ahead of practical considerations, after it emerged that Brussels has threatened to kick Britain out of its Galileo satellite navigation programme, which it helped to fund.
He also revealed the cabinet was still split over the "backstop" proposals, which would keep the whole of the UK in the customs union until a permanent solution is found to the Irish border issue.
It comes as Jeremy Corbyn criticised Theresa May over the government's delay in laying out its Brexit plans in more detail, demanding when the government will publish its white paper on the UK's future relationship with the EU.
Labour is facing its own Brexit troubles as splits emerged over plans to shift its approach to leaving the EU.
Ahead of a Commons showdown on the government's flagship legislation, the Labour leadership has sought to quell pro-EU rebels in the ranks, by tabling a bid for a Norway-style deal where Britain retains full access to the single market.
However critics said the efforts were "nowhere near enough", and called for support for a cross-party amendment from the Lords, which could effectively keep Britain in the single market.
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Worried EU car manufacturers are already in talks about rejecting British-made parts because of Brexit, an industry leader has revealed.
The growing fear was that “lots of jobs disappear” because of Theresa May’s vow to leave the existing customs union, the head of a component supplying firm said.
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The Prime Minister's official spokesman told a Westminster briefing: "The backstop is there for if we have reached an agreement but extra time was required to implement it.
"But as the PM and others have said, we do not expect that to be the case."
Asked if David Davis had threatened to resign over the issue, he replied: "Not that I'm aware of, no."

Brexit and Security
RUSIA senior member of the Cabinet will discuss security co-operation post-Brexit. The speech will be streamed on this webpage. ,Theresa May has told Israeli counterpart Benjamin Netanyahu she is concerned about the shooting of Palestinians during a wave of protests at the Gaza border.
The prime minister stressed she recognised Israel's right to self-defence but called on Mr Netanyahu to take action to alleviate the situation.
The Israeli prime minister insisted that the protests were driven by militant group Hamas and the response was aimed at minimising causalities.
The pair are also at odds over the Iran nuclear deal, with Mrs May restating the UK's commitment to the agreement, which Israel opposes and US President Donald Trump has pulled out from.
Rival groups of protesters gathered outside Downing Street waving Palestinian and Israeli flags ahead of Mr Netanyahu's arrival.
Ms May told him the UK was "concerned about the loss of Palestinian lives" in the recent Gaza protests.
She said the UK "absolutely recognises" the right that Israel has for self-defence against the activities of "extremists and terrorists".
"But with 100 Palestinian lives lost and a deteriorating situation in Gaza I hope we can talk about how we can alleviate that situation and how we can ensure that we can get back to a position where we are able to find a way through to talk about a two-state solution."
Mr Netanyahu insisted protesters were being "paid for and pushed by Hamas" to try to break through the border and kill Israelis.
"This is not a non-violent protest, quite the contrary," he said.
"We are doing everything we can to both minimise casualties and at the same time protect Israeli lives."
Mr Netanyahu has lobbied for European leaders to follow Mr Trump's example and pull out of the Joint Comprehensive Plan of Action (JCPOA) Iran deal.
But Ms May said: "Along with France and Germany the UK continues to believe that is the best route to preventing Iran from getting a nuclear weapon.
"We will remain committed to it as long as Iran meets its obligations.
"But we do recognise that there are other issues that need to be addressed in relation to Iran - its destabilising regional activity in countries like Syria and Yemen and also the the proliferation of ballistic missiles."
Mr Netanyahu told the prime minister he was focused on making sure Iran did not get a nuclear weapon and "how to roll back Iran's aggression in the region".
"I think we can find ways to work together to achieve both goals," he said.
"Each year 54,000 women lose their jobs because of pregnancy and maternity discrimination, while fathers are worried that taking shared parental leave will negatively affect their careers.
"This is unacceptable. If we are serious about building fairer and more family-friendly workplaces, then employers must be transparent about how they support parents in the workplace through their parental leave and pay policies.”
The Prime Minister cannot be trusted to protect workers' rights after Brexit, a senior union boss has said.
Frances O'Grady, general secretary of the TUC, said workers should not "pay the price" of leaving the EU, whichever way they voted in the referendum.
She told the annual conference of the Fire Brigades Union in Brighton: "The TUC is demanding a cast-iron guarantee that rights at work will be safe.
"British, Irish, French and German unions campaigned hard to win that level playing field of rights, like holiday pay and parental leave, right across Europe, and we're not going to stand by and let this Tory Government trash them.
"Theresa May promises those rights will be protected and enhanced after Brexit. We don't trust her."
Ms O'Grady said Brexit-supporting ministers Boris Johnson and Michael Gove were not bothering to disguise their real agenda.
"They've already briefed their media friends that Brexit is a great opportunity to get rid of the EU Working Time Directive.
"That means limits on long working hours, the right to paid holidays and protection for night workers, and we're kidding ourselves if we think they'll stop there.
"We respect the referendum result, but we want a deal with the EU that protects jobs, livelihoods and rights at work that keep pace with our friends elsewhere in Europe."
Theresa May's official spokesman confirmed that the proposal would include a time limit on any interim arrangement to keep the border open in the absence of a more permanent solution, but declined to give further details.
He stressed that the Government does not believe that the backstop option will have to be put into effect, as ministers think that a better customs arrangement can be agreed before the UK's withdrawal from the EU.
The Government's position
Britain should withdraw from the European single market and customs union, to enable it to strike new trade deals around the world. It should forge a new "deep and special partnership" with the EU27, with free trade and close security links.
Who supports it? Theresa May and a large majority of Conservative MPs, along with some Labour rebels.
The Labour position
Labour wants Britain to remain in "a customs union" with the EU after Brexit, to ensure tariff-free access and frictionless trade with the remaining 27 members. Jeremy Corbyn's new policy would also make "full access" to the EU internal market an objective in Brexit negotiations.
Who supports it? Labour's leadership, including Mr Corbyn and shadow Brexit secretary Sir Keir Starmer, who are expected to be backed by most of the party's MPs.
The 'soft Brexit' option
Keeping Britain inside the customs union and the single market, to maintain the closest possible ties with the EU. Amendments passed by the House of Lords, and due for an MPs' vote next Tuesday, would require the Government to try to negotiate a customs union and continued membership - alongside non-EU countries like Norway - of the European Economic Area (EEA).
Who supports it? A majority of peers, along with europhile MPs from all parties linked to the Open Britain campaign, such as Tory former minister Anna Soubry. A substantial number of Labour MPs, including Chuka Umunna, believe the party should back the cross-party Lords amendments, despite orders from the leadership to abstain in the EEA vote.
The 'Exit from Brexit' option
Offering voters the opportunity to reverse their decision to leave the European Union.
Who supports it? This is the official policy of the Liberal Democrats and the favoured outcome of the Best for Britain pressure group and the People's Vote campaign for a second referendum on the final Brexit deal.
The 'No Deal' option
Britain leaves the EU without any agreement on future relations, and trades on World Trade Organisation terms.
Who supports it? Only a relatively small number of committed eurosceptics in Parliament regard this as their preferred result, but many MPs - particularly on the Tory benches - believe the Government should be preparing for the possibility of a "no deal" exit in order to strengthen the UK's hand in negotiations with Brussels.

