Theresa May is on a fresh collision course with Brussels after the government said it would give MPs the chance to override a key part of the exit deal agreed with the European Union.

In a new bid to win over Tory rebels, ministers announced they would support moves to ensure parliament is given a vote in 2020 on whether or not to enter the controversial Northern Ireland backstop.

That could see MPs vote to block the UK entering the backstop, even though it would be legally bound to do so under the terms of the withdrawal agreement.

The government said on Wednesday that it will accept an amendment tabled by former Tory minister Sir Hugo Swire.

The motion says that if no trade deal with the EU is in place by 2020 ministers must hold a vote in parliament on whether or not to enter the backstop, and must limit the UK’s participation in the mechanism to one year.

Both appear to contradict the terms of the withdrawal agreement with Brussels, which states that the backstop is the default option if a deal on the future relationship is not in place by the end of 2020 and says that this will apply indefinitely.

UK efforts to secure a time limit on the backstop were firmly rebuffed by the EU, and European officials are likely to be angered by the government supporting Sir Hugo’s attempt to introduce a unilateral time limit.

Confirming the decision to support the plan, Ms May’s spokesperson said: “The amendment means that if parliament were to choose not to commence the powers needed to implement the backstop, then the government would have to find another way to meet its obligations under the withdrawal agreement, which are to prevent a hard border in relation to Northern Ireland.

“That legislation would need to be passed by parliament.”

He suggested there were “alternative ways, including technology, of avoiding a hard border”, which would still allow the UK to meet its legal obligation to do so.

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Under the terms of the withdrawal agreement, the UK and EU must attempt to strike a deal on their future relationship before the end of 2020.

If that is not possible, they will either trigger the backstop, which sees the UK enter into a temporary customs union with the EU, or will be able to extend the transition period for a maximum of two years to allow for a deal to be completed.

Any decision made by the UK in relation to the backstop or an extension of the transition period would need to be approved by the EU. If the two sides could not agree, the matter would go to independent arbitration.

It is thought that, while the UK would still be legally obliged to enter the backstop if there is no alternative, even if MPs vote against it, the political pressure would be so great that ministers would likely have to try to agree an alternative plan with the EU.

Stephen Barclay, the Brexit secretary, admitted that accepting Sir Hugo’s amendment would not be enough to satisfy angry Brexiteers but said that, together with new plans to give the Stormont Assembly a “strong role” in managing the backstop, it marked a “welcome step forward”.

He told the Commons: “I recognise that that alone will not be sufficient for all of the concerns that colleagues may have, but I think it is a welcome step forward.”