Foreign secretary tells Andrew Marr he agrees with former health secretary’s figure of at least £5bn being available by 2020

Boris Johnson has said the NHS will get substantial extra funding after Brexit, despite Theresa May’s refusal to endorse the leave campaign’s promise of an additional £100m a week.

The foreign secretary strayed from his brief during BBC1’s Andrew Marr show to sign up the prime minister to a cash injection for health services during this parliament.

During the leave campaign, one of Johnson’s central arguments was that leaving the EU would allow the UK to pump an extra £350m a week into the NHS, a figure that was later revised down to £100m. However, May declined to back that promise this month when she travelled to the G20 in Beijing.

Johnson was pressed on the extra money for the NHS after Andrew Lansley, the former health secretary, suggested at least £5bn could be available to the NHS after Brexit. Asked whether the government could guarantee a “really substantial” extra amount of money per week for the NHS by 2020, Johnson said: “Well, yes, in the sense that clearly once we leave, and that isn’t possible until the final moment that of the change in our arrangements, and we take back control of the budgets we contribute to the EU.

“Once that happens, clearly it will be possible for the UK government to spend people’s money on our priorities. And the number one priority for most people is the NHS. It sounds to me Andrew Lansley has got it right.”

Johnson also aired his views on when the UK should leave the EU, despite No 10 sources making clear last week that this was a decision for May alone. He said the process should not be allowed to drag on and the UK should be out before May 2019 to avoid a new batch of British MEPs being elected to Brussels. That would imply article 50 would have to be triggered before May next year to allow two years of negotiations to take place.

“There’s Euro elections coming down the track, and people will be wondering whether we will be wanting to send a fresh batch of MEPs to an institution we are going to be leaving,” Johnson said.

He was not pressed on whether the UK should pursue a “hard” Brexit outside the single market with greater powers to restrict immigration, or “soft” Brexit preserving single market access but with fewer migration controls. He accused British businesses of being addicted to cheap migrant labour, claiming that for 25 years they had been “mainlining immigration like drugs” without caring enough about training young people from the UK.

The appearance on Marr was the first major interview given by Johnson since he became foreign secretary in May’s government, after pulling out of the contest at the last minute when his campaign chief, Michael Gove, decided to challenge him.

The former London mayor has kept a relatively low profile since the referendum, leading to speculation that he is being kept on a tight leash by No 10.

On Sunday, an account of the EU referendum campaign by David Cameron’s former communications chief, Craig Oliver, revealed that Johnson was genuinely conflicted about whether to back leave or remain until the very last minute and accused him of being a “conflicted inner”. The account, in a book serialised in the Mail on Sunday, says Johnson vacillated, sending conflicting text messages to Cameron the day before he came out for Brexit.

Oliver wrote: “I ask DC what makes him so sure Boris is wobbling. He reads out some parts of the text, including the phrase ‘depression is setting in’, followed by a clear sense that he’s reconsidering. Neither of us is left in any doubt.”

The following day Cameron received a final text from Johnson saying he would be backing leave – just nine minutes before he publicly announced his intentions in a chaotic press conference outside his London home.

Oliver said Cameron later phoned him to say Johnson’s final message had been clear that he did not expect to win, believing Brexit would be “crushed”. “He says Boris is really a ‘confused inner’, and their previous conversations confirmed that view to him,” he wrote.