It’s a curious truth that the last government, which boasted far more first- and second-generation citizens of this country in high office than any previous administration – a visible triumph of postwar multiculturalism and integration – should have defined itself so raucously and divisively in its opposition to immigration. Nadhim Zahawi, who was one of those figures, and held a dizzying number of ministerial posts in quick succession as Tory administrations imploded (he was Boris Johnson’s chancellor for his last 24 hours in office) – describes himself in the title of this memoir as The Boy from Baghdad. The bleak irony of the fact that he served in cabinets that dehumanised refugees for political ends is nowhere mentioned.

Instead, Zahawi makes an impassioned case for the entrepreneurial resourcefulness and determination that migrants bring to the economy. “In the UK,” he writes, “it’s not uncommon to meet people who’ve fled politically or physically dangerous situations and made huge sacrifices for the sake of their family. Get in an Uber and you could lay money on meeting one. We take for granted these people will mop our floors and take care of our sick, but when you think they were the ones brave enough to leave, it woefully underestimates their capabilities. Harnessing that energy is just one of the reasons we need safe and legal routes for those fleeing persecution and tyranny.” Hear, hear, you may say; though if that sentiment was as vociferously expressed while Zahawi was chairman of the Tory party, it was drowned out in his colleagues’ shrill focus on hostile environments and ”stop the boats” and the Rwanda plan.

This vividly written memoir gives you a bullish flavour of some of the obstacles that Zahawi overcame on his own journey here. He hesitates to call himself a political refugee, arguing that “somehow I feel like it’s a label that should be reserved – protected – for people who haven’t been as lucky as me”, and wondering “can a person be both refugee and a ‘rich man’?”

He was born into a powerful family in Baghdad. His great-grandfather had been the grand mufti; his grandfather the governor of the Central Bank of Iraq and minister of trade. His father, who ran a construction business, spent the summer as a young man by the Thames, where the family rented a house in Barnes. All that changed, however, with the coup that brought Saddam Hussein and his Ba’ath party to power. When Zahawi was 11, his father was forced to flee overnight to London to escape arrest. Other acquaintances and distant family members were not so lucky. “In the years since,” he writes, “I’ve met many people whose stories didn’t end the way ours did that day. Families whose fathers were tortured. Wives who were raped. Children who were murdered. Our neighbour whose uncle no longer talks on account of the fact the party cut out his tongue.” One result of that, despite everything, is that Zahawi remains an unrepentant supporter of British involvement in the Iraq war. “In 200 years’ time,” he writes, “I don’t think we will consider it a mistake.”

The change in the Zahawis’ fortunes was compounded by his father’s disastrous investment in a startup company; when that went bankrupt and the family lost their house, they moved into a flat owned by other exiles from Iraq (Zahawi eventually married that family’s daughter). That second fall from grace brought out the fighter in him (channelling aggression from bit parts in football hooliganism in his teens). With friends, he started a series of businesses as he worked for a chemical engineering degree – a venture selling T-shirts that changed colour in the heat turned over £16m, he claims. That spirit brought him to the attention of Jeffrey Archer, who became his political mentor. (When he collaborated with the peer on a controversial charitable drive that claimed to raise millions for persecuted Iraqi Kurds, Archer called Zahawi and his best mate “Bean Kurd and Lemon Kurd”.) His stint on Archer’s campaign team in an ill-fated run for London mayor led to the creation of YouGov, the first internet polling company, with Stephan Shakespeare.

The genesis of that business, Zahawi’s decision to gift the bulk of his shareholding to his father, who held it offshore, led to the financial scandal that ultimately ended his political career. Though you suspect that a desire for exoneration was one motivation for this book, he saves his excuses for the penultimate chapter here, making fairly unconvincing efforts to explain how he became the first chancellor of the exchequer to have to repay £5m to HMRC.

Before we get to that bottom line, like any decent city accountant, Zahawi emphasises all the items on the credit side of his political balance sheet. He was overlooked by David Cameron for ministerial office for eight years, but eventually established a profile as a man for a crisis, by then the Tories’ only growth industry. During the pandemic he oversaw the “ventilator challenge”, which saw British companies manufacture 15,000 machines in short order for the NHS; he then became the minister responsible for the vaccine rollout. Johnson, to whom he remained loyal, right up to the last gasp, liked to call him, as part of his Churchillian fantasy, “his Beaverbrook”, a reference to the infamous wartime head of procurement.

That aura persisted even after the first stories about Zahawi not fully disclosing the HMRC investigation broke. Liz Truss subsequently entrusted him, as chancellor of the duchy of Lancaster, to chair the queen’s funeral arrangements. It says a good deal about that government that its “safest pair of hands” was a man who blames a £5m hole in his tax returns on “not paying more attention to the paperwork”.

• The Boy from Baghdad: From Waziriyah to Westminster by Nadhim Zahawi is published by HarperCollins (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply