The British Parliament’s House of Lords has approved an amendment to the country’s "Brexit" bill that would guarantee European Union citizens’ residence rights after Britain leaves the 28-member bloc.

The amendment isn’t likely to clear Parliament’s lower chamber, the House of Commons, where members of Prime Minister Theresa May’s Conservative Party dominate. But disagreements between these two chambers could threaten Ms. May’s goal to begin the Brexit process by the end of March, when the government hope to trigger Article 50 of the bloc's Treaty of Lisbon.

But by voting in this amendment to the bill, the House of Lords highlighted concerns about post-Brexit uncertainties for the 3 million Europeans living in the United Kingdom today. Ineligible to vote in the June 23 Brexit referendum, they could stand to lose the most when Britain leaves the EU.

The government has said repeatedly that it plans to allow EU nationals to remain in Britain if its own expats get that same right in the rest of the EU. One Conservative member of the House of Lords, Michael Howard, said he favors starting the process, then "negotiat[ing] to give these people the rights they deserve to stay in this country."

But with the Brexit process expected to take years, many critics say that doing so would cause too much uncertainty. Europeans living in Britain "need to know now, not in two years' time or even 12 months' time," what their rights are, said Dianne Hayter, the Labour Party's Brexit spokeswoman in the House of Lords, according to the Associated Press. "You can't do negotiations with people's futures. They're too precious to be used as bargaining chips."

While Britain hasn’t yet triggered Article 50 of the Lisbon Treaty, which would begin its exit from the EU, the non-British European nationals who call the UK home are already worried about their futures – particularly highly skilled workers in sectors that often rely on EU funding and collaboration with institutions on the continent.

“I have started questioning whether the UK is where I want to build my future and whether I'm wanted here,” one European woman who graduated from Oxford and now works at an aerospace company in Britain told The Christian Science Monitor last October. Even if permitted to stay, some say, they wonder how attitudes toward foreigners may change post-Brexit.

She and other expats didn’t have a voice in the Brexit referendum, but aren't the only ones feeling excluded. On the other side of the Channel, the estimated 1.2 million Brits living in Europe could vote – if they had resided in Britain within the past 15 years. In the run-up to the vote, PRI’s The World reported that this cutoff left some longtime expats feeling left out of a historic decision.

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Enough Lords agreed with Ms. Hayter to pass the amendment through Parliament’s upper chamber. But with Conservatives likely to strike it down in the House of Commons, and with both houses needing to concur before the Brexit bill can become law, the Lords could soon need to decide whether to press their position on residence rights.

This report contains material from the Associated Press.