A row over immigration erupted tonight as it emerged that free movement of people from the European Union to the UK could last for “many years” after Brexit.

In a White Paper spelling out more details of its plan for a post-EU Britain, ministers said immigration controls would be phased in, raising the prospect of Theresa May going into the next election with still open borders.

Pro-EU campaigners said the announcement appeared to show free movement would last for “many years”, even though the Government was willing to sacrifice the UK’s membership of the single market in the meantime. Ukip said it showed the public would conclude the Tories were not “serious about taking back control” of Britain’s borders.

The White Paper, which set out the Government’s 12 key goals for Brexit, says Britain will regain control of its borders by leaving the freedom of movement directive, but does not mention reducing the number of people coming to the UK.

It says that “openness to international talent will remain one of our most distinctive assets” and that the UK “will always want immigration”.

The Government says that MPs will get a say in drawing up the plans for future control of numbers, promising Parliament an “important role”.

“There may be a phased process of implementation to prepare for the new arrangements. This would give businesses and individuals enough time to plan and prepare for those new arrangements,” it says.

There is little public detail about what the planned immigration controls will actually involve. The Government has ruled out implementing a points-based immigration system as promised by the Leave campaign.

Joe Carberry, co-executive director of Open Britain, which campaigns for a soft Brexit, said: “The Government is sacrificing our valuable place in the single market for an apparently vital end to free movement, which now may not happen for many years.

“The only real conclusion from an otherwise thin White Paper is that there is no mandate for, or merit in, allowing immigration policy to drive economic policy.

“The Government would be far better served negotiating for full participation in the single market and arguing for reform of free movement of labour on a Europe-wide basis.”

Ukip's immigration spokesperson John Buckley MEP said that the Government had failed to set out concrete plans for reducing immigration, even though “most” Brexit supporters wanted to see it reduced.

“Based on the Conservative Government’s utter failure to bring down immigration to their promised ‘tens of thousands’ the public would be right to conclude from today’s White Paper that the Government isn’t serious about taking back control of our borders and immigration any time soon.

“Will the Government make an immediate commitment to take back total control of our borders and immigration by the end of the Article 50 negotiation and no later than 2019?”

The White Paper says the new immigration system will “encourage the brightest and the best to come to this country, as part of a stable and prosperous future with the EU and our European partners”.

It continues: “It is important that we understand the impacts on the different sectors of the economy and the labour market.

“We will, therefore, ensure that businesses and communities have the opportunity to contribute their views. Equally, we will need to understand the potential impacts of any proposed changes in all the parts of the UK.

“So we will build a comprehensive picture of the needs and interests of all parts of the UK and look to develop a system that works for all.”

Making a statement to the Commons on the White Paper, Brexit Secretary David Davis appeared to confirm that the UK would quit the European customs union, but did not give any further information on the specific arrangements could be introduced to replace it.

In her Lancaster House speech on Brexit, Theresa May said Britain could seek to maintain “associate membership” of the customs union, but would seek an arrangement that would allow it to strike trade deals with other countries, something customs union members cannot do.

Asked to confirm that the UK was “definitely leaving the customs union”, Mr Davis said the White Paper made clear the intention to “exclude ourselves from the common commercial policy and the common external tariff, which amounts to that”.

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The White Paper states that different transitional arrangements of varying lengths could be necessary for different sectors of the economy and the wider negotiation, from cars and food products to free movement of people.

But it adds that: “The interim arrangements we rely upon are likely to be a matter of negotiation. The UK will not, however, seek some form of unlimited transitional status. That would not be good for the UK and nor would it be good for the EU.”

Disputes over trade and regulations are arbitrated by the European Court of Justice. The White Paper makes clear the UK intends to completely leave the court’s jurisdiction, but says a new dispute resolution mechanism will be needed to ensure “uniform and fair enforcement of agreements” – possibly via an arbitration panel.

Labour’s Helen Goodman said proposals to leave the customs union were having a “devastating impact” on the manufacturing industry.

The Bishop Auckland MP said: “You said we would have meaningful votes on a whole range of things.