Britain's upper house of parliament on Tuesday inflicted a new defeat on Prime Minister Theresa May\u2019s government, challenging her decision to fix a date next year to leave the European Union. The House of Lords voted for an amendment to a draft law, removing a proposed fixed time for a Brexit departure of 11 p.m. on March 29 next year. The government has already set the clock ticking on a two-year exit process that has so far failed to deliver a divorce deal and which was damaged by her gamble on a snap election which cost her party its majority in parliament. Some lawmakers criticised the government's plan to impose a specific date for Britain leaving the EU, saying it would create significant difficulties if negotiations with Brussels went down to the wire. "It creates a rod for the UK negotiators' backs, weakens any UK negotiating position, and adds unnecessary pressure to those in the executive trying to deliver Brexit in a coherent measured fashion," said Arthur Wellesley, a Conservative member of the House of Lords, who introduced the amendment. "We should give ministers a bit more flexibility to secure and obtain ratification of the best possible deal which will do the least damage to the economy and the national interest." This is the 12th time in recent weeks that the government has been defeated in the House of Lords on the draft legislation that will formally terminate Britain's EU membership. The vote can be overturned by the lower house, the House of Commons, but underscores the deep divisions over Brexit across parliament and could encourage lawmakers who hope to derail May's plans to forge a new relationship with the EU. Earlier, opposition parties in the Lords and rebels in May's Conservative Party voted in favour of the amendment that means Britain should participate in EU agencies after leaving the bloc next year. The government has proposed retaining membership of some EU agencies for medicine, chemicals and aviation while leaving others after Brexit. Britain is likely to leave the EU police agency Europol and lose automatic membership to bodies like the European Maritime Safety Agency and the European Environment Agency. Agencies that oversee Europe's banks and pharmaceutical sector have announced they will move from London to cities on the continent after Brexit, highlighting potential job losses for Britain's economy from leaving the EU. After the Lords, the bill will return to the House of Commons. Both houses have to agree on the final wording of the bill before it can become law. Lawmakers will have to decide whether to back the government or reject the law \u2014 with the risk that Britain could crash out of the EU next year without any deal in place. This is the penultimate session for the bill in the upper chamber during the report stage, where members have already voted in favour of amendments including to compel ministers to seek a form of customs union with the EU.