The government’s decision to postpone the publication of a key document relating to its plans for the UK’s post-Brexit immigration system has been called “hugely frustrating” by British businesses.

The immigration white paper, which was originally scheduled to be published last summer, will not be released until after the transition deal is done, the Home Office confirmed on Monday. This could be early summer and means negotiations due in Brussels this week on the rights of new EU migrants to Britain after March 2019 will get under way with little prior public discussion of the options.

It also means that a Brexit immigration bill, promised in the Queen’s speech, will not reach the statute book before the registration of the 3 million EU nationals already living and working in Britain gets under way this autumn.

Ministers face an urgent question in the Commons on Monday tabled by Yvette Cooper, the chair of the Commons home affairs committee, who described the postponement as “completely unsustainable”.

Josh Hardie, the deputy director-general of the Confederation of British Industry (CBI), said businesses would be “hugely frustrated” by the postponement.

“Firms need time to plan for change and that is why many will be deeply disappointed by any delays to the white paper. It is perfectly possible to be clear on people’s rights to work in the UK, for the transition period at least.

“The government should commit now that people’s rights to work won’t change over the first two years from our date of departure from the EU.”

Cooper said: “The government has been promising this white paper for months. Ministers told the home affairs select committee it would be published before Christmas.”

She said the delay was completely unsustainable. “EU citizens living here, employers, immigration staff, border staff and parliament all need to know what the government intends,” she said.

“Even if the long-term plans need to wait until the migration advisory committee reports or until the negotiations on the future relationship, we still need to know practical questions about the government’s intentions for registration and transition that are now little more than a year away.”

Theresa May said last week that Britain wants new EU migrants who arrive in the UK during the transition period to lose any right to settle after the post-transition Brexit day in March 2021.

But a leaked draft of the immigration white paper, disclosed by the Guardian last September, showed the Home Office wanted to go further and ban jobseekers from qualifying for residence permits and require new EU workers to pass a minimum income threshold test as well provide evidence of a job offer. It is not known if British negotiators intend to press these points in the coming weeks.

European students coming to study in Britain after March 2019 will also want reassurance of being able to stay more than two years to complete their three- or four-year courses without having to apply again for a residence permit.

A Home Office spokesperson confirmed the postponement saying: “We are considering a range of options for the future immigration system and will set out initial plans in the coming months. In December, we reached a deal with the EU on citizens’ rights – and our priority now must be to agree the detail of the implementation period.”

It is understood that the terms on which new EU migrants can come to Britain after March 2019 will now be set out in a renamed EU withdrawal and implementation bill to be published after the current round of talks are completed. Although they are scheduled to be finished by the end of March it is expected they will go on to April or May.

It is expected that the immigration white paper detailing exactly how Britain’s immigration system will work after full Brexit will then be published after the transition/implementation deal has been done. That could be early summer in June or July. It would then be followed by a much delayed immigration bill setting out the new system.

The registration of the 3 million EU nationals can be done through secondary legislation – statutory instruments – which are approved by parliament with little debate as registration schemes are allowed under existing EU laws.

The decision to postpone the main Brexit immigration bill also means that Theresa May will avoid a damaging defeat over moves to remove overseas students from the annual net migration target. Plans to challenge government policy on this issue on which May is nearly isolated in the cabinet were drawn up on the basis there would be an immigration bill to amend.

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