Boris Johnson’s conduct in office could still sink him despite his buoyancy in opinion polls, Gordon Brown has said, recalling the demise of Margaret Thatcher three years after a landslide election victory because “mistakes … caught up with her”.

The former Labour prime minister, speaking to the Guardian as he publishes a new book, also praised the climate movement, #MeToo and Black Lives Matter and predicted huge electoral changes across the world that he said would be led by the young.

“People are being tested through this crisis. I think you’re going to see big changes in personnel at the end of it,” he said. “I would be looking for people whose names we don’t know yet to come through in the next year or two … it’s going to be a younger generation, who are going to sweep aside some of the conceptions of the older leaders.”

Brown has been deeply critical of the conduct of senior political figures during the lobbying scandals that have engulfed the Conservative party, arguing for stronger safeguards. His new book, Seven Ways to Change the World, sets out the global cooperation needed to tackle the climate crisis, nuclear proliferation, tax havens, inequality and emerging public health threats.

The book is a foray into the current political sphere, inspired by what he describes as his “deep shock” at how global leaders reacted to the Covid pandemic – with isolationism and an eye on competition rather than international cooperation.

Brown said he believed the UK was far better prepared for a pandemic in the early 2000s than it was when Covid-19 hit.

“I think we were better prepared [then] than the government was 10 years later,” he said. “Too few people have focused on the cuts in health service budgets, and the cuts in our capacity to prepare for things. So I don’t think that we’re prepared nationally in the way we should be but I also don’t think we were prepared internationally. And that’s because cooperation broke down.”

Brown said politicians worldwide, most notably the then US president, Donald Trump, saw cooperation as weakness. “You’ve got populist politicians really believing that cooperation is actually some sort of betrayal of national interest when in fact it is the only way in the modern world of actually advancing the national interest,” he said.

Brown said he did not share the deep pessimism of many in progressive politics about Johnson’s enduring popularity despite the catalogue of errors in dealing with the pandemic and scandals around his personal conduct.

“In 1987 when she got a massive majority, people thought Mrs Thatcher could go on for ever and by 1990 she was out. The mistakes that she was making caught up with her,” he said.

“It takes time for people to see what is really going on. It might look, if you take a picture of today, [that] Boris Johnson can survive all the mistakes that have been made. But I think when you look at it over a period of years, I’m not sure that that’s going to be the same response. And it’s a bit like a fast-moving train that … can pick up speed but then suddenly, suddenly, it grinds to a halt.”

Hinting that it was a progressive platform that Labour could learn from, Brown praised the response of the US president, Joe Biden, to the pandemic, who offered a major economic stimulus while also “realising the danger of being drawn in by rightwing extremists into culture wars”. He said Biden’s agenda was one he had hoped to set in 2009 in response to the financial crisis.

“In one sense he is doing now what I wanted to do in 2009 which we couldn’t really get off the ground,” Brown said. “In 2009 this fiscal orthodoxy, this idea that debt and deficits were unacceptable, prevented people actually taking the action that was necessary. We didn’t have public support for it, and of course austerity was the consequence.”

Brown said he believed the world was at a critical moment, both over the next few months when global leaders had opportunities to make major new agreements on health, vaccine provision and the climate, and in the next few years when he predicted the influence of youth-led movements would grow.

He said he feared like many parents that the world his teenage sons would grow up in may be worse than for his own generation. “They’ve grown up with a global financial crisis, a climate change crisis, a pandemic, Brexit and a disruption of our international relations,” he said. “But at the same time, I see in young people a greater determination than perhaps our generation had to sort things out.”

He said movements such as Black Lives Matter had already caused seismic shifts in public thinking. “These are the major changes which are perhaps not reflected in what politicians are doing at the moment, but will over time be the pressure points for political change in our country and around the world.

“A younger generation have had to live through some terrible events and tragedies that you never thought would happen in one decade, but actually are determined to do something about it, and to some extent they think our generations failed their generation, they want to be the generation that will make the changes.”