The cross-party committee said in a report published Monday that legislation could leave people in a "precarious situation" and that it raises significant human rights concerns. "
The Committee argues that 3 million EU citizens will be left" in a rights limbo subject to subsequent negotiations. "
It also warns that the rights of Irish nationals in the United Kingdom under the law on Immigration and social security (EU withdrawal) can be "diminished", for example by limiting their ability to live in the UK with a non-EU spouse.
The committee has drafted amendments to the bill to ensure rights The report recommends that citizens' rights be protected by primary legislation instead of relying on ministers introducing statutory instruments after Brexit.
"We are talking about the rights of persons who have lived in the UK this year, decades into the our social security system or even been born in the UK and lived here throughout their lives, "said MP Harriet Harman, President of the United Kingdom Me nneskerettighedsudvalg.
"When it comes to rights, promising that everything will be drafted in the future is not good enough, it must be a guarantee why the committee has reinstated rights guarantees back in the wording of the bill."
Until 31 December 2020, EU citizens have to apply whether or not there is a Brexit agreement.
However, the report of the MPs raised concerns about the lack of physical evidence of status under the scheme and the deadline for individuals to register.  "Getting the right one is extremely important considering the similarities in some of these concerns with problems encountered in the treatment of the Windrush generation," the report says, referring to the difficulty of proving citizenship to the descendants of the first large group of Caribbean immigrants to arrive in the UK in the 1940s.
"These could be people who have lived and worked in Britain throughout their lives," it concluded. "Their rights should not depend on subsequent registration with a scheme within a specified period."
The British Government has promised harder immigration rules for those who want to move to the country. May has promised to complete the free movement of EU citizens as part of the Brexit Agreement.
After Brexit, EU citizens wishing to come to the UK will "seek permission and receive European temporary residence" in order to stay longer than three months, said home secretary Sajid Javid in a statement in January.
"EU citizens wishing to stay longer than three years will have to make a new application under the new competency-based future immigration system, which will begin from 2021," he added.