Theresa May has vowed to overturn a key change to her Brexit legislation imposed by the House of Lords, which she claims could stop Britain leaving the EU.

The prime minister said that when the proposed change comes back to a vote in the Commons the government would be “robust” in trying to block it.

But her spokesman could not give a clear answer on Tuesday as to whether government whips believe they have the support of enough MPs in the Commons to overturn the change.

It comes as Ms May prepares for a Brexit meeting with select cabinet ministers on Wednesday, at which they will try to come up with a joint position on post-withdrawal customs relations following the EU’s rejection of the UK’s existing proposals.

Ms May met with her full cabinet on Tuesday after suffering the decisive defeat in the Lords, which she argued will give parliament “unprecedented powers” to direct her administration’s course.

The prime minister’s spokesman said after the meeting of top ministers: “Cabinet expressed its strong disappointment at the defeats inflicted on the EU Withdrawal Bill in the House of Lords, saying they risk tying the government’s hands behind its back in negotiations with Brussels.

“The prime minister said that when the bill returns to the House of Commons the government would be robust.

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“She said it was vital to ensure the legislation is able to deliver the smooth Brexit which is in the interest of everybody in the United Kingdom.”

Ms May has said she will give parliament a vote on the Brexit deal she agrees with the EU, but has warned that if it is rejected the UK will crash out of the bloc with no deal.

Given that the government’s own economic projections suggest this would be the worst possible outcome for the country, critics have accused Ms May of using the threat as leverage to get MPs to back her deal regardless of what it is.

But the amendment passed by the Lords to Ms May’s EU Withdrawal Bill on Monday, would mean that if her deal is rejected, then it is parliament that will decide what happens next – with any option open.

The prime minister’s spokesman said: “What the amendment which was passed last night would do, is weaken the UK’s hand in our Brexit negotiations by giving parliament unprecedented powers to instruct the government to do anything with regard to the negotiations – including trying to keep the UK in the EU indefinitely.”

But twice asked if the prime minister is confident she actually has the numbers in the Commons to reverse changes, the spokesman said only that it is in the “interests of the Houses of Parliament” to allow the government to deliver Brexit.

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Ms May has already suffered a defeat at the hands of Tory rebels in the Commons, meanwhile the next stages of other pieces of Brexit legislation have been delayed because the government is unsure it can defeat amendments placed by Conservative backbenchers.

However, the No 10 spokesman said the government is determined to have EU Withdrawal Bill passed in the same state that it left the Commons the first time round, indicating that it will try and overturn all of the changes imposed by the Lords.

It has suffered seven defeats in the Lords in recent weeks, imposing changes to its legislation which if left untouched could lead the way to keeping the UK in a customs union, keeping the EU’s charter of fundamental rights and restricting the “Henry VIII” powers, which the Bill gives to ministers to make new laws without full parliamentary scrutiny.

The cabinet’s Brexit subcommittee will meet to discuss the vexed issue of post-Brexit customs relations on Wednesday, with at least one of its members having suggested they will quit if the UK remains in a customs union with the EU.

International trade secretary Liam Fox hinted strongly that he would resign if the prime minister gives way to pressure in parliament and opts for closer customs relations with the EU after Brexit. He refused to answer the question directly over whether he would quit, but added: “Getting no answer you can draw your own inferences.”