Queues for petrol and mass slaughter of pigs at farms because of a lack of abattoir workers are part of a necessary transition for Britain to emerge from a broken economic model based on low wages, Boris Johnson has argued.

His comments, on the first day of the Conservative conference, came as Liz Truss, the foreign secretary, insisted it was the role of business, not ministers, to sort out such problems.

“I don’t believe in a command-and-control economy, so I don’t believe the prime minister is responsible for what’s in the shops,” Truss told a conference fringe event. “This is why we have a free enterprise economy.”

Speaking earlier, in a pre-conference TV interview, Johnson acknowledged that disruption to some supplies could continue until Christmas, but said the only short-term solution was to resume uncontrolled immigration, which would be wrong.

The Petrol Retailers Association (PRA) said on Sunday that the crisis was “virtually at an end” in Scotland, Wales, the north of England and the Midlands, but warned supplies were still not getting through to London and the south-east.

The prime minister refused to completely rule out further tax rises, saying he would not increase them further “if I can possibly avoid it”.

Asked about warnings of the imminent slaughter and incineration of up to 120,000 pigs because of labour shortages across the UK, Johnson initially argued that this was no different from what normally happened to livestock.

Speaking to BBC One’s Andrew Marr show, he said: “I hate to break it to you, Andrew, but I’m afraid our food processing industry does involve killing a lot of animals, that is the reality. Your viewers need to understand that. That’s just what happens.”

When Marr pointed out that it would be different, as in this instance the pigs would not be butchered for food and the farmers would receive no income, Johnson said this was part of a wider transformation of the economy post-Brexit.

“If I may say so, the great hecatomb of pigs that you describe has not yet actually taken place. Let’s see what happens,” he said.

“What we can’t do … in all these sectors is simply go back to the tired, failed old model, reach for the lever called ‘uncontrolled immigration’, get people in at low wages. And yes, there will be a period of adjustment, but that is, I think, what we need to see in this country.”

Asked whether labour shortages and the associated disruption they caused were an inevitable part of his Brexit policy, Johnson did not disagree. He said: “When people voted for change in 2016, and when people voted for change in 2019, they voted for the end of a broken model of the UK economy that relied on low wages and low skill, and chronic low productivity. And we’re moving away from that.”

Later on Sunday evening, Johnson partly blamed the lorry driver shortage on industry bosses making it an undesirable career for women, saying they did not want to have to sleep in a small cabin and urinate in bushes.

The prime minister suggested if more women had been attracted to the job, that would have helped make “a huge difference to our current situation”.

Speaking at a rally organised by the Women2Win organisation during conference, Johnson asked: “Why is it, do you think my friends, that it’s so difficult to persuade people to become lorry drivers and join the road haulage industry? Why should they join when you can’t even … you have to urinate in the bushes.

“I’m speaking frankly about this, why should you when you have to sleep in your cabin, that’s not frankly what women want. It’s ridiculous.

“That is the result of chronic, chronic under-investment in that sector of industry, chronic failure to deal with the issues, chronic mainlining of low-wage and low-skill talent rather than investing in equipment and investing in facilities and encouraging women to take part. That would have made a huge difference to our current situation.”

Chris Loder, a Tory MP, told a fringe meeting at the party conference that it would be a good thing for supermarket supply chains to “crumble”, even if it caused short-term problems.

Asked by Marr about a prediction by the chancellor, Rishi Sunak, that shortages of petrol and other goods could last months, to Christmas or beyond, Johnson initially refused to answer. Pressed by Marr, he said: “Rishi is invariably right. But it depends how you interpret what he said.”

Johnson said the issue was a long-term one, caused largely by the road haulage industry not investing in better pay and conditions and instead relying on the cheaper labour of drivers from Europe, now largely gone as a result of Brexit.

Johnson also defended his government’s tax rates after Marr said that with the highest taxation policies since the 1940s, he was less like Margaret Thatcher and more like Harold Wilson.

He said: “You’re talking total nonsense, because neither of those distinguished people had to deal with a pandemic on the scale we have. Neither of them had a fiscal meteorite hit their system on the scale that we had.”