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LONDON (Reuters) - The House of Lords passed an amendment on Wednesday calling for the government to negotiate a customs union with the European Union, giving Prime Minister Theresa May a potential new headache in her Brexit plans.

The upper parliamentary chamber backed a cross-party amendment to a trade bill, calling for the government to take all steps to enable the United Kingdom to participate in a new EU customs union after it leaves the bloc.

May has ruled out any such union which would be an anathema to eurosceptic MPs in her Conservative Party, although the idea has the support of some pro-EU Conservatives and the Labour Party.

The Trade Bill, which focuses on transposing outside countries’ trade deals with the EU into bilateral deals with Britain, is due to be passed before Britain leaves the bloc on March 29.

The Lords’ amendment can be overturned by parliament’s elected House of Commons but it means MPs could now have a vote on the issue and boost the hopes of those who want a Brexit which sees Britain still closely aligned to the EU.

May’s divorce deal was overwhelmingly rejected by MPs in January and she has promised to bring back a revised version by March 12, although talks at securing changes have made no headway according to EU officials.

If her treaty is rejected again, MPs will then be given the chance to vote for a no-deal Brexit and for extending the date of the divorce.