Sandi Toksvig on QI, Stephen Fry and her open wedding

Then there’s a new novel, also coming out next year, End of the Sky, a sequel to last year’s Slice of the Moon, about the Irish Famine. She is the chancellor of the University of Portsmouth, president of the Women of the Year assembly and patron for the Corporate Alliance against Domestic Violence among other roles.

And let us not forget 15 to One, the general knowledge quiz show she hosts on Channel 4. In addition she did the News Quiz on Radio 4 for 23 years – the last nine as host – but gave it up last year to found the Women’s Equality Party (of which, more anon). And last but not least, she is now taking over from Stephen Fry as the new host of the brainy comedy quiz show QI.

Toksvig hosting the News Quiz for the last time in 2015

At home, which she shares with her psychotherapist wife, Debbie, she may knock up Stilton soup of an evening (“the trick is to put in more cheddar than Stilton”) or do the plumbing.

How much plumbing can she actually do? “Whatever you need!” she says. “You want a kitchen put in, I’m your girl. I’m very handy and I love a practical challenge. I fit all the stereotypes of the lesbian with power tools.”

Of course, she has hobbies: weaving (she has just invested in a second loom, which allows her to do smaller pieces more quickly) and knitting.

She also somehow finds time to see her three children from her previous relationship with Peta Stewart – Jessica, 27, who runs a successful photography business; Megan, 25, a junior doctor; and Theo, 22, who has just graduated from drama school: “They are the great love of my life.”

The conversation gets round to tattoos at one point, and Toksvig says she is thinking of getting one: “I’d like to have three Nordic runes of my children’s initials underneath my watch. It would be invisible but I’d know it was there.”

Toksvig, who is shy despite her “show-off” job, is not a fan of parties. “I haven’t got the patience for small talk although, I once saw a woman standing on her own in the corner and I realised it was Monica Lewinsky and I had the nicest evening with her – she was charming. But mostly I’m totally happy in my own space at home with the door closed with my family and friends.”

We are in a Soho private members’ club, post photographs, and I have been shooed out of the room – “You don’t want to see me in my underwear, do you?” – while Toksvig changes from one top with a slogan on it (WOMAN) to another (WONDER).

Toksvig was in that talented gang at Cambridge whose members included Emma Thompson, Hugh Laurie and Stephen Fry himself, among others. “I suppose what it means, in a way, is that the silly bits of your life – the famous bits – none of us take too seriously with one another,” she says.

Because you’re all famous, although some are more famous than others, aren’t they? “Yes,” that familiar Toksvig head-tilt that presages a joke, “I wonder what happened to Emma? Something secretarial I heard.”

Fry was “a brilliant, fantastic and genial host but the show, itself, is the thing,” she says of her QI predecessor. In terms of their different styles at the helm, Toksvig reckons Fry is more “professorial” while she is more likely to be “the encouraging teacher”.

“It is the most brilliant blend of entertainment and education. To be old-fashioned about it, it is Reithian in its principles. It is really perfect telly – and my dad, who was a fantastic broadcaster, never saw the show but would have thought it was the pinnacle of what one ought to be trying to achieve.

“It’s obviously arcane and odd and fascinating, and there’s a lot of what I call ‘take away’ from the show, as in ‘I didn’t know that, I want to remember that forever’. Did you know, for instance, that female trout fake orgasms? Well, there you are – it’s not just women in the world! It’s trout, as well.”

Sandi, do you know the meaning of callipygous? “No.” Perfectly formed buttocks. “I’ll give you another one,” she smiles, “dasypygal – the condition of having hairy buttocks. So we can have a whole buttocks section on QI.”

Thankfully, Toksvig has increased her energy levels recently, otherwise she surely couldn’t have coped with her current life. Two years ago, she lost a lot of weight. Was it hell? “ No, actually, not once I made up my mind.”

As she tells it, her mind was made up for her because of serious health issues. “I felt so ill. Like I was just going to die. Honestly, if I’d forgotten something upstairs, however expensive it was, I’d have rather bought a new one than go up and get it.”

The decisive factor was when she developed plantar fasciitis, an inflammation of the foot. “I was in so much pain, I was walking with a walking stick – it affects the muscle that holds the whole foot together and I had it in both feet. I was in agony. I was sobbing every day and I couldn’t get out of bed without being in pain.”

So she went to see a physio – “a woman of mature years who I will be grateful to for the rest of my years” – who told her new patient, quite bluntly, “‘Look, I’ve been doing this for a really long time so I tend to say what I think. You have plantar fasciitis because you are fat. If you weren’t fat, you wouldn’t have it.’

“And I thought, ‘Wow! Nobody’s ever spoken to me like that!’ and I went away and lost four stone. And now I run and I lift weights and box with Debbie and I’ve never done anything like that before.”

The main change is that “I can bound up that flight of stairs now”. And without taking any drugs!

“OK, I have a scoop for you about my drug use.” No, surely not – can our national treasure really have a buried 'My drugs hell' story?

“A friend of mine said to me, ‘Look, Sandi, you’ve never done drugs, it’s ridiculous, you should try some.’ So she baked me some cannabis biscuits” – this is said with the precision of a Downton dowager – “and said, ‘Go away for a weekend.’ This was many years ago... So me and my then partner splashed out on a very expensive bed and breakfast for the weekend. We went down Friday night, had half a biscuit – slept till Sunday! Missed the whole weekend.”

After we have recovered from this story, we move on to more serious matters, such as the Women’s Equality Party. When we last met in 2009, Toksvig was a firm Liberal Democrat supporter, and said, “I want to retire from showing off, but I don’t want to retire from doing something useful with my life. So I’m not saying it’s out of the question that I may have a political career in the future.”

The WEP policy launch party in 2015

She felt that she had to give up her beloved News Quiz as, were her political party successful, it would obviously be in the news. Was it worth it? “I am really proud of the party,” she says. And then lists its achievements to date: 70 branches across the country, thousands of members, the tireless campaign for equal pay.

Equal pay... “Yes, wouldn’t it be nice if we thought, 45 years after the Equal Pay Act, that it was a good idea!” May I ask a cheeky question, in that case? Are you being paid the same salary as Stephen for hosting QI? “That, you would have to ask them,” she says. “I challenge you to ask the BBC. Certainly if you are doing the same job it seems a bit absurd if you’re not paid the same.” (I asked the production company who make QI for the BBC and was told they don’t comment on such matters.)

We talk about Theresa May as prime minister and Toksvig’s views on “the glass cliff”, as opposed to the glass ceiling. It’s the idea that when things are completely messed up and seem beyond repair, as in Iceland’s financial crisis or our recent Brexit mayhem, that’s when women are called upon to fix it. “If the woman succeeds, that’s marvellous – and if she doesn’t, it’s all her fault.

“The men who got us to where we are now, which is having decided to leave [the EU] with no plan as to how that might happen – whether you are in favour of it or not – have all stabbed each other soundly in the back and then swum away as fast as their blood loss will allow.

“So it’s very interesting to me that a woman has been put in charge and she’s the sort of woman you want in charge. She’s slightly nanny-ish and she’s the daughter of a vicar – and the truth is we didn’t vote for her.

“I’ve met Theresa May and I think she’s a good person. I’m not someone who goes ‘ooooh boooo, the Tories’ or ‘ooooh boo’ anyone actually. You sit down and have a sensible conversation and she is really, really capable of having a sensible conversation. So, good for her. But do I think it’s a glass cliff? Absolutely I do.”

Sandi Toksvig and Theresa May attend The 61st Women of the Year lunch and awards 2016

Toksvig has been a Hillary Clinton fan for a long time and as for Donald Trump... “Donald Trump or Hillary Clinton? Seriously? Do you know what I mean?” she raises an eyebrow. “I’d rather elect the soap dish that I use when I travel... I seriously think a small plastic soap dish would be better at leading the United States than Donald Trump.”

I wonder whether she has a new public crush, as when we last met it was former Girls Aloud singer Cheryl. “No, I’ll just keep with Cheryl,” she says. “I’m such a loyal person and I love my wife so much it’s ridiculous, so I don’t really look at anyone else. Cheryl just looks like she’s really nice. I don’t want to sleep with her, I just want to say hello.”

Does it feel strange saying “my wife”? “In my lifetime, I never thought that would happen so I’m thrilled that I can even have this conversation,” she says.

On that note, before we part, I wonder why – as a self-proclaimed shy person – she opted to have such a public wedding, at the Royal Festival Hall in London in 2014. She doesn’t hesitate. “I still get people who are gay coming up to me and telling me how they are rejected either culturally or by religion or by their family – and just because the law changed, it didn’t change everybody’s perception.

“I felt we needed to be bold and happy and brave on the day and to make a big, public statement and say ‘It’s OK’ to the frightened gay or lesbian person – it was to try to make them feel better. It was actually just me and Deb and 150 family and friends and then I said, ‘Anyone who wants to come, help yourself ’ and two and a half thousand people turned up! Deb was terrified and said, ‘I’m only doing this if I can be dressed by Vivienne Westwood’ and Vivienne said yes so we were good to go.”

You know what? Sandi Toksvig just needs to have both slogans on the one T-shirt, because she actually is Wonder Woman.

QI with Sandi Toksvig starts tonight at 10pm on BBC2