The European parliament has said EU citizens living in the UK after it leaves the bloc risk discrimination in jobs and housing, because the government will not issue physical documents under the settled-status scheme.

In a resolution backed by a resounding majority of MEPs in Strasbourg, the parliament said the British government’s “conflicting announcements” about special status had caused “unhelpful uncertainty and anxiety” for EU nationals who had made the UK their home.

EU fears have mounted since the Home Office minister Brandon Lewis told a German newspaper last October that EU nationals risk being deported if they fail to apply for special status, the scheme to secure their rights as UK residents, by the end of 2020.

MEPs are especially worried about the design of settled status, an e-registration system, which does not provide EU27 nationals with papers or ID cards. The absence of documents, the resolution said, increased the risk of discrimination against EU27 nationals by prospective employers or landlords “who may want to avoid the extra administrative burden of online verification or erroneously fear they might place themselves in an unlawful situation”.

One parliament source said the absence of physical documents spelled “complete Windrush trouble for citizens’ rights”, a reference to the scandal in which Commonwealth-born citizens were denied work, healthcare, benefits and even deported to countries they hardly knew, despite spending decades as tax-paying legal residents of the UK.

The EU is also concerned about a decision by Boris Johnson’s government to change the design of the independent monitoring authority, which is being created under the withdrawal agreement to safeguard the rights of EU citizens. The parliament said the government needed to ensure that the authority would be “truly independent” and up and running on the first day after the UK leaves the transition period.

The EU’s chief Brexit negotiator, Michel Barnier, told MEPs on Tuesday that the European commission would be “particularly alert” to difficulties in obtaining the new residency status. “I have and will continue to insist in particular on the importance of the UK putting into place a strong independent monitoring authority,” he said. “An authority that must be able to act rapidly and fairly when faced with complaints of [European]Union citizens and their families.”

The resolution was passed with 610 votes, including those of British Labour, Liberal Democrat and Green MEPs. Only 29 MEPs voted against, mostly members of Nigel Farage’s Brexit party. A further 68 MEPs abstained, including British Conservative MEPs.

The government, which has launched a multi-million-pound advertising blitz intended to show the ease of securing settled status, had received nearly 2.6m applications by the end of November. More than 2.3m of those cases had been concluded, with 59% granted settled status and 41% granted pre-settled status, a category that applies to EU nationals who have lived in the UK for under five years.

Pre-settled status gives people the same rights to live and work in the UK, but means they must reapply for settled status and maintain continuous residence. Only five applicants have so far been turned down for any form of status.

UK government sources argue that the scheme has been unfairly criticised; they have highlighted the contrast between the cost-free UK process and the three-figure charges facing UK nationals trying to secure their rights in some EU member states.

The withdrawal agreement does not require the UK government to give papers or ID cards to EU27 nationals, and government sources say discrimination by employers or landlords would be illegal.

The European parliament also pledged to monitor the situation for 1.2 million British residents in the EU. Many face a slew of bureaucratic hurdles, such as minimum income requirements for self-employed people, costs and charges of getting documents, as well as uncertainty about their status because of delays after applications.

Barnier said the commission would do its “utmost to ensure that the rights of 1 million British citizens living in the 27 member states are guaranteed; that each and everyone of them is properly informed and supported”.

The MEPs have also urged EU leaders to explore “how to mitigate” UK citizens’ loss of EU citizenship rights. Guy Verhofstadt, the European parliament’s Brexit coordinator, has previously urged a special EU citizenship scheme for British nationals, but the idea has been dismissed by decision-makers as a political and constitutional non-starter.

Verhofstadt has called on MEPs to back the Brexit withdrawal agreement, the final legal step in Britain’s formal EU exit.

He released his formal recommendation on Wednesday, advising MEPs to back the deal on 29 January. “The withdrawal of the UK is a regrettable moment for the European Union and for our integration process, but we can only respect the sovereign decision of the British people,” the text stated. It added that the divorce agreement “organises the separation with the less [sic] harm possible for both parties”.

A Home Office spokesperson said: “We have done far more [for EU citizens] than any other EU member state has done for British citizens, and it’s time they adopted a similarly generous approach. We have already provided certainty to 2.5 million people who have been granted status through the EU settlement scheme. It’s free, there’s plenty of support available, and it provides a secure digital status, which can’t be lost, stolen or tampered with.”