“When I looked down,” she recalls of one visit, “it was so totally shocking to see our little oasis of Gombe… It looked like a dust bowl: completely bare hills, overfarmed, more people living there than the land could support.”

Today, however, as a result of the Lake Tanganyika Catchment, Reforestation and Education Project, which her Institute began in 1994, the Gombe chimps now have “three to four times more forest than they had ten years ago. It’s regenerated so quickly. So we have 30-foot-high trees.” I feel better already.

More than half a century since she first engineered improvements to the conditions of the chimpanzees at London Zoo, Goodall is still fighting hard on behalf of captive chimps too. In the 1980s, she raised ethical concerns about their use in xenotransplanation, which led the medical community to steer away from this practice. More recently, she has worked with Francis Collins, Director of the National Institutes of Health in the US, to phase out their use of captive chimpanzees in medical research; she is delighted the US Senate voted to increase the budget available for retirement of these chimps. “We are beginning to win,” she says.

I ask Goodall if she is in favour of a blanket ban on the use of chimpanzees in medical research. “I can’t quite say that. But what I can say is that, ethically and morally, I feel it's wrong to use them, and it’s absolutely wrong to put them in five-foot by five-foot cages.”

Goodall puts chimps at the forefront of the wider debate about the use of experimental animals. “At one time, the scientists said we’ll always need animals for this – and now we don’t,” she says. “If science really puts its mind to getting alternatives… once they do, they’re cheaper and usually safer.”

With our time almost up, I realise I haven’t asked after Mr H, the toy monkey who famously travels with her from one venue to the next. Somehow Goodall the activist doesn’t seem complete without him, and I wonder if he might join us.

Mr H stands for Mr Gary Haun, a US marine who lost his eyesight in a helicopter crash at the age of 21, then went on to became a professional magician, climb Mount Kilimanjaro, scuba, sky-dive, and much else besides. “He thought he was giving me a stuffed chimp for my birthday,” Goodall recalls – but the soft toy has a tail, so is clearly a monkey. “Gary,” she told him, as she guided his hand towards the evidence of his mistake, “I know you can’t see it… but you have no excuse.”

For the last 20 years, Goodall has kept Mr H close as a reminder of another of her reasons for hope: “The indomitable human spirit… He’s been to at least 60 countries with me, he’s been touched by at least four million people. I say that when you touch him, the inspiration rubs off.”

Goodall invites me to touch Mr H – but instead of inspiration, I have a sudden, parental panic that he might one day go missing. “I’ve nearly lost him several times but that’s the original,” she says, stroking him gently. Once, she left him on the top of a telephone kiosk in an airport and had boarded her plane before she realised. “I’ll have to get off the plane,” she explained to the attendant, adding: “You’ll have to bolt me in to keep me because I’ve left my most precious object outside.”

Still clutching Mr H, Goodall reaches into her bag and another soft toy peeps out. “This is Cow” – a gift handed to her during a recent visit to the dairyland state of Wisconsin. “I was going to give Cow to the next deserving child,” she explains, but instead she has turned her into “a spokesperson” for abused farm animals. She looks at the toy and then talks about it as if she’s giving it praise. “Cow has worked really hard – she has created I don’t know how many vegetarians, even in places like Argentina where they live on meat.”

I am reminded of something I’ve read: how Goodall, as a child, loved to arrange tea parties for her soft toys. I wonder if there are others who would like to join us – but it turns out that Jubilee, her childhood chimpanzee, is in Germany, being fitted for a jumpsuit to hold his failing stitching in place.

Goodall herself is flying to Germany in a few hours. “I’m going to Düsseldorf, then Vienna, then back to Munich… It still amazes me. Children write to me and say, ‘You taught me, you did it, I can do it too.’ So this is why I have to go on going around. Because it’s making a difference.”