MPs might have to vote on the Brexit deal without knowing details of the future immigration policy, Sajid Javid has said, as he also indicated the planned scheme might abandon the target of keeping net annual migration to the tens of thousands.

In a sometimes testy appearance before the home affairs select committee, the home secretary said only that the long-awaited white paper on post-Brexit immigration should arrive before the end of the year.

“The government hasn’t set a final publication date for the white paper, but very shortly,” Javid told the cross-party panel when asked when it would arrive. “I’d certainly say in December.”

Asked whether it would come before MPs vote on the Brexit deal on 11 December, Javid said: “I hope it will come before that, but I’m not in a position to be too specific on the date right now.”

Some committee members expressed disquiet that the Commons might have to decide on the Brexit deal without knowing a key policy element. Javid was then reminded by the committee chair, Labour’s Yvette Cooper, that he had earlier promised the document by the end of July.

“When I first came into the department I was hoping that things were more ready than they actually were,” Javid said.

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Quizzed later in the session by the former Labour MP John Woodcock on whether the white paper would stick to the Conservatives’ long-broken pledge to reduce annual net migration below 100,000, Javid declined a series of opportunities to do so.

“The white paper is not complete. So you will have to wait for its publication,” Javid told Woodcock, who quit the Labour party in July amid a disputed disciplinary case.

Javid said: “What you call the target, the ambition, that was set out in the Conservative party manifesto, is for this parliament. In terms of what might be the future immigration policy vis-a-vis targets and numbers and aspirations, you’ll have to wait and see.”

He added: “What you’ll see in the white paper, speaking broadly, is a future immigration system that is really fit for the future for the long term. That means it has got to be flexible enough to meet our needs in how they change over time.”

Pressed by Cooper on how realistic the target would be when non-EU net migration alone is currently 230,000 a year, Javid called the figure “an aspiration”. He said: “It is our policy to bring down net migration to more sustainable levels, and our aspiration is the tens of thousands.”

Asked whether that tens of thousands target formed part of the post-Brexit EU immigration policy, Javid would only respond: “I have answered your question. I am trying to bring down net migration overall.”

A final area of confusion centred on JJavid’s statement that freedom of movement for EU nationals would end immediately if the UK left the EU in March without a deal.

Committee members questioned how this would work, when the government has already said that in this case, border checks would not immediately change, and employers would not be obliged to check the position of EU nationals seeking work until a post-Brexit “settled status” scheme was completed.

“The two are perfectly compatible. It’s perfectly possible to end freedom of movement in law, and not put an extra burden on employers after that date,” Javid said.

Asked for more details, he said: “We will be actually setting this out in due course, because it is important we set out more detail on how that might work.”