Hillary Clinton is sequestered in a hotel room, giving a big television interview, when Mary Beard arrives at Claridge’s. While she waits outside on the sofa, though, it quickly becomes clear that the star of this conversation is the classicist. One by one, members of Clinton’s staff approach in reverent tones to declare her their heroine. Even a passing cameraman stops to pay court and say: “I love you!” Does this happen to Beard all the time? “Yes,” she laughs, “funnily enough, it does.”

Since the Cambridge professor began presenting TV programmes on the Romans nearly a decade ago, she has become world famous, as well as wildly popular for her robust refusal to stand for misogynistic online abuse. Trolls are publicly challenged; one was memorably shamed into taking Beard to lunch to apologise for calling her “a filthy old slut”. Her latest book, Women & Power: A Manifesto, brings an illuminating historical perspective to the contemporary abuse of powerful women. (Our meeting takes place in mid-October, before the #metoo revelations had begun to gather pace.)

Clinton is in London to talk about What Happened, her rivetingly candid if shell-shocked account of her defeat to Donald Trump in last year’s US presidential election. As soon as she appears, it becomes very hard to believe she lost because voters found her cold. She greets Beard with a whoop of delight, exclaims, “This is fun!” does a very, very funny impersonation of Trump’s voice and, over the course of an hour, laughs a lot.

Once seated, the physical contrast between the two women is arresting. Clinton folds her hands carefully before her and confines her movements to slow nods of the head, while Beard gesticulates energetically as she talks, her whole upper body pitching and swaying. But the chemistry between them crackles, and Clinton conveys the impression of someone keen to see what she can learn from the academic. ...