But he was reluctant to say Britain should put a cap on overall numbers, and suggested that unhappiness over immigration was down to the government’s failure to make the right arguments to win public consent.
Johnson’s comments give an insight into how he could approach the issue of immigration if he succeeds David Cameron as Tory leader and prime minister in the event of a Brexit vote.
He said the government had been less than honest with people about the nature of immigration and failed to appreciate the impact on schools, the NHS and other public services.

But he would only say the numbers of new arrivals should not have been so high without the agreement of voters.
“To add a city the size of Newcastle to the UK every year … let me put it this way, it’s too high to do without consent,” he said. “That is the issue. There is no consent. It might be that a party or government or politicians could persuade people if they believed that it was a good thing and it turbo-charged the economy and all the rest of it. What is not acceptable is to say there’s nothing we can do, that’s just the way it is.”
On Thursday data on national insurance numbers is expected to reveal that more EU citizens are working in the UK than are recorded in official statistics.

Boris Johnson on board the Vote Leave bus. Photograph: Darren Staples/Reuters
In his latest swipe at David Cameron, who is campaigning in favour of remaining within the EU, Johnson said: “I think it has been misleading, there is no question it’s been misleading. I think politicians have been driven into this terrible dishonesty about it by the EU’s arrangements.”
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