Leave campaigners had claimed quitting the bloc would help slash net migration.
But now they fear a fresh surge of migrants rushing to beat a March 2019 deadline.
Chancellor Philip Hammond indicated there will be no cut-off for the free movement of people until the two-year divorce process is complete.
He told the BBC: “Of course they can come here after today – we remain full members of the EU with all the obligations and all the rights of membership.
“What happens today is that we formally begin the process of negotiating our exit from the European Union.
“But we remain full members of the European Union for the next two years, subject to all the rules and obligations of membership.”
As a full member, the UK must accept free movement of people around other countries.
Latest figures show immigration in the year to September 2016 was estimated to be 596,000, including 268,000 EU citizens, 257,000 non-EU citizens and 71,000 British citizens returning home.
It included the highest level ever recorded of Romanians and Bulgarians – 74,000 – coming to Britain.
Net migration – the difference between those arriving and those leaving – was running at 273,000.
Brexiteers toured the country last year saying EU membership meant uncontrolled immigration from the other 27 countries.
Many pro-Leave voters believed Brexit would trigger a quick plunge in net migration.
But their hopes of early limits on arrivals from the EU appeared to be dashed.
Campaigners hit out at the lack of a deadline for migrants coming to the UK in the Prime Minister’s letter to EU Council President Donald Tusk triggering Article 50 .
Leave Means Leave chairman Richard Tice said: “There was one key point missing from the letter – no mention of any cut-off point for EU migration.
“This is deeply worrying as it could lead to an influx of mass migration to Britain in the two years between now and March 29, 2019.
“The British people voted to take back control of their borders and the Government must deliver on that now.”
Mrs May’s letter to Mr Tusk said only: “We should always put our citizens first.
“There is obvious complexity in the discussions we are about to undertake, but we should remember that at the heart of our talks are the interests of all our citizens.
“There are, for example, many citizens of the remaining member states living in the United Kingdom, and UK citizens living elsewhere in the European Union, and we should aim to strike an early agreement about their rights.”
The Prime Minister’s spokesman said the Government wanted to seal a quick deal on citizens’ rights.
But he added: “We have said very clearly right from the outset of this process that while we are members of the European Union we will fulfil our obligations and responsibilities.
“The fact is we are going to honour our obligations and commitments while ever we are a full member of the European Union.”
Meanwhile, Mr Hammond also put Britain on collision course with Brussels over its demand for a £50billion divorce payment.
“I should be clear that we simply do not recognise some of the very large numbers that have been bandied about in Brussels,” he said.
March 29th, 2017: Mirror