The home secretary, Amber Rudd, has sought to reassure businesses over the Brexit transition. Photograph: Andrew Milligan/PA

EU nationals will still be able to come to the UK during a transitional period after Brexit but must go through a registration and documentation process, Amber Rudd has said.

The home secretary reassured businesses that there will be no cliff-edge in the migration system when the UK officially leaves, after Brandon Lewis, her junior minister, said free movement would officially end in 2019.

Lewiss remarks caused a stir because Michael Gove and other senior political figures had said the cabinet was effectively united on allowing free movement to continue during an implementation phase for two to four years after 2019.

Rudd said free movement would end as a point of principle in March 2019 because it is part of being in the EU. But arrangements very similar to free movement could still carry on during the implementation phase lasting until around 2022.

There will be an implementation phase when new EU workers will need to register their details, Rudd said, adding that the full, new EU immigration policy would come into force only after this transitional period is over.

Rudd has commissioned the migration advisory committee to help work out what this final immigration system could look like, asking it to examine the costs and benefits of migration from the EU.

In her letter to the committee, she said: As part of a smooth and orderly transition as we leave the EU, the second phase of our immigration proposals is based on a temporary implementation period to ensure there is no cliff-edge on the UKs departure for employers or individuals During this period there will also be a straightforward system for the registration and documentation of new arrivals.

After this implementation period, we will move to the third phase, which will be our long-term arrangements covering the migration of EU citizens, designed according to economic and social needs at the time, and reflecting our future deep and special partnership with the EU. The government will want to ensure that decisions on the long-term arrangements are based on evidence. The commission that we are now asking the MAC [migration advisory committee] to undertake is very much part of this.

The government has already suggested it will ask all EU citizens currently living in Britain to officially register their interest in acquiring documentation allowing them to live and work in the country after 2019 when Britain is scheduled to leave the European bloc.

Rudds decision to commission her migration advisers a year after the Brexit vote was criticised by leading opposition figures as far too late. The committee will not report until September 2018 just six months before the UK leaves the EU.

Yvette Cooper, the chair of the Commons home affairs committee, said it was staggering that it has taken a year since the EU referendum for the government to finally commission the migration advisory committee to assess the potential impact of one of the most important issues facing our country ahead of Brexit.

The MAC has now lost 13 months in which they could have been working on assessing the EU migration issues for each sector and for the economy as a whole, and the impact of different policy changes. Delaying basic research like this, yet still promising its all going to be sorted out by March 2019 is completely irresponsible, she said.

The fact that the government has taken so long to ask these basic question must either be incompetence or internal disagreement. But neither bode well for the design and implementation of any new system to replace it.

Diane Abbott, the shadow home secretary, said it was right the government was seeking objective analysis but it must commit to publishing the report in full once it was finalised, for scrutiny in parliament. There must be no repeat of the buried Home Office reports into international students, or the Saudi funding of terrorism. And there should be no attempt to reform the immigration system until the report has been published and debated.

It was also noted that Rudds remit letter to the migration advisory committee contained no mention of Theresa Mays target of reducing numbers of new arrivals to the tens, not hundreds of thousands a year an aim held since 2010.

Lewis confirmed the target still exists but refused to say it would be reached within this parliament.

Labours Pat McFadden, a supporting member of the Open Britain group fighting for a soft Brexit, described the governments position as a shambles.

Only hours after the home secretary announces there will be no cliff edge when we leave the EU, her immigration minister announces a definite end to freedom of movement from March 2019, he said.

This mornings announcement throws a grenade into attempts to reassure the country that there will be no Brexit cliff edge. Yesterday, it was a row about chicken. Now its immigration. Ministers are contradicting one another by the hour. The country needs good leadership during this crucial period. It is certainly not getting it.

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EU nationals can register to enter UK during Brexit transition - The Guardian