They fear the EU is poised to weaken its stance on the issue at a make-or-break summit next month in order to keep negotiations moving between London and Brussels.
Controversial issues including the future rights of EU citizens to bring in family members, the rights of their children born after Brexit, and compulsory new criminal record checks.
EU nationals in Britain say new “settled status” rules will reduce their rights and be based on UK immigration law – exposing them to the Home Office’s self-described “hostile environment” towards immigrants.
A Government minister recently admitted EU citizens could be deported before being able to challenge any rulings that they are not entitled to stay after Brexit.
Key issues will be “shunted” into phase two of the talks, rather than being settled before the negotiations move onto future trade terms between the UK and the EU, MEPs and citizens fear.
They spoke with The Independent after meetings with Michel Barnier, the EU chief negotiator, who will recommend whether “sufficient progress” has been made to progress the talks.
It comes as the Prime Minister prepares to hold a crucial lunch meeting with Jean-Claude Juncker, the Commission President, and Mr Barnier in Brussels on Monday.
Before meeting Ms May, however, the pair will hold talks with Guy Verhofstadt, the European Parliament’s Brexit coordinator, to discuss progress in the negotiations.
In recent weeks, the two sides have moved closer to agreement on both a financial settlement and the Irish border – with less focus on citizens’ rights, the third “divorce” issue.
Seb Dance, a Labour MEP and a member of the Parliament’s EU Citizens’ Taskforce, said: “Michel Barnier did not go far enough. There are concerns that the EU is ready to dilute its stance on citizens’ rights – but we won’t sit back and let that happen.
“Family reunification is one of the areas that the EU may be ready to compromise on.
“We can’t move on just for the sake of moving on. We should only move on when we are certain that nobody will suffer as a result because of a…