Post-Brexit attempts to limit immigration and uncertainty during negotiations with Brussels could spark a "surge" in arrivals, a Commons report suggests.
MPs called on the Government to set out a cut-off date and end uncertainty for EU nationals who are already in the UK, warning they must not be used as "bargaining chips".
Following the outcome of the referendum last month, Britain is expected to seek to introduce controls on free movement rules but the details of the system are yet to be outlined.
A report from the Home Affairs Committee said: "Past experience has shown that previous attempts to tighten immigration rules have led to a spike in immigration prior to the rules coming into force.
"Much will depend on the negotiations between the UK and the EU and the details of any deal to retain or constrain the free movement of people and the rights of those EU/EEA citizens arriving in the UK and UK citizens living in the European Union."
Ministers were urged to move quickly to establish certainty over the status of EU citizens and any new rules on free movement.
The committee said the outcome of the referendum "has placed EU nationals living in the UK in a potentially very difficult and uncertain position", adding: "EU citizens living and working in the UK must be told where they stand in relation to the UK leaving the EU and they should not be used as bargaining chips in the negotiations."
The report also called for "an effective cut-off date" to avoid a surge in applications, adding the "most obvious" options include the date of the referendum, the date Article 50 - the formal mechanism to leave the EU - is triggered, or the date when the UK actually leaves the bloc.
EU citizens settled in the UK before the chosen date should be afforded the right to permanent residence, the report said.
It added that establishing where EU nationals live and work is the "first step in the process of clarifying their right to permanent residence in the UK".
The report said: "The first option may be registration, a second may be identification by National Insurance number. Whatever scheme the Government follows should be chosen as quickly as possible and be made as seamless as possible."
Labour MP Keith Vaz, chairman of the committee, said the migration is "the biggest issue relating to Brexit".
He added: "There is a clear lack of certainty in the Government's approach to the position of EU migrants resident in the UK and British citizens living in the EU.
"Neither should be used as pawns in a complicated chess game which has not even begun. We have offered three suggested cut off dates, and unless the Government makes a decision, the prospect of a 'surge' in immigration will increase."
The report raised concerns about the Government's ability to increase capacity sufficiently to meet its commitment to resettle 20,000 Syrian refugees by 2020 and highlighted the approach to asylum-seeking Eritreans, saying: "It is unacceptable that the Home Office is still getting so many of its decisions regarding nationals of this country wrong."
A Government spokeswoman said: "We have been clear that we want to protect the status of EU nationals already living here, and the only circumstances in which that wouldn't be possible is if British citizens' rights in European member states were not protected in return.
"We are about to begin these negotiations and it would be wrong to set out further unilateral positions in advance.
"But there is clearly no mandate for accepting the free movement of people as it has existed up until now."