The delivery is classic Mid-late 20th-Century Dad: straightforward, unsentimental, practical "Y'mum's poorly, boy. It's terminal," Webb writes of the encounter in How Not to be a Boy.
"It's 'orrible, boy, but that's life. Now, I don't know if you want to come and live with me or . . . " he looks around the kitchen, "I mean, you're probably going to need a cleaner, Derek, because . . . well, it's hard keeping a place clean." Derek nods. "Josie, who cleans my house, she could probably come and do a couple of hours a week."
Webb, 44, tries to be fair to his dad. His father had his problems, he says, but part of the reason was that he didn't have a sound model of fatherhood because his own father didn't provide one. We can only be the men we learn to be.
Asked now how he thinks his dad would have received the book, Webb says, "I think the key part there was that I couldn't possibly have written it while he was still around."
When he was 19 and living with his dad, two years after the death of his mum, Webb went
into a local pub and ran into an older guy, who said he was told in the 1970s to, "look up Paul Webb. You won't find anyone better for drinking, f***ing and fighting."
The guy appears not to realise that a boy might not admire these qualities in his father. In fact, he seems to think Webb might be somehow proud of them. And he's right. Webb liked that his dad was recognised for being good at something, even though he hated what that something was. Being a man is complicated.
How Not to Be a Boy is a memoir, trading on its author's success as a comedy actor and writer, primarily on TV shows Peep Show and That Mitchell and Webb Look, but its overriding theme is Webb's sense that he never matched the images of masculinity he saw all around him: tough, sporting, emotionally stoic.
He has an odd group of imaginary childhood friends called The Guy-Buys and is always the second last picked for football, just ahead of a boy with cerebral palsy. Later, he develops a liking for books and drama and has sexual fantasies about his - male - best friend.
He says that the book's project, if it has one, is to encourage a conversation about what it means to be male, to ask hard questions that maybe aren't asked enough, about how we should be.
He mentions studies that have demonstrated that when parents place newspaper birth announcements, they're more likely to express pride in a boy's arrival and happiness in a girl's, and that they're actually slightly less likely to announce a girl's arrival at all.
He also mentions research showing that parents look forward to having their babies for gendered reasons: fathers look forward to teaching sons sport and mothers look forward to personal intimacy with daughters.
Boys, he writes, are "expected to be more independent, more aggressive, more outward-facing and less interested in personal relationships" than girls, from even before they're born.
The project of reshaping and rethinking of what it means to be male appears gaining momentum. Where Webb says he felt he was starting a conversation when he started writing the book two years ago, now he feels like he's joining one.
He talks of the work of Prince Harry, who admitted earlier this year that he had suffered his own mental health struggles for which he sought counselling, and who has also founded a charity to combat stigma about mental illness.
Webb also discusses public intellectuals like novelist Matt Haig, who has written and spoken openly about his depression, and cross-dressing artist Grayson Perry, who has made success high-profile television shows about mental health and gender identity.
This willingness to discuss what it means to be a man may itself be some sort of breakthrough for a gender noted for its preference for "banter" and "having a laugh" rather than "conversation".
"If something terrible happens to you," Webb writes in How Not to be a Boy, "And you're lucky enough to have supportive friends, there will be a period when you hear a version of this several times a week: 'And if you need to talk, I'm right here.'"
"There are times when we're all grateful to hear this, and other times when we experience it as pressure. And although I've no doubt that there are many women and girls who have the second reaction, I think it's men and boys in particular who get into trouble here. We feel grateful for the kindness, but helpless and frustrated. 'Talk about what? What's to talk about? Talking won't change anything, will it?' Suddenly we're surrounded by well-meaning people encouraging us to talk about our feelings. The problem is, talking about our feelings is something we've been specifically trained not to do."
"Drinking, f***ing and fighting" as Paul Webb was admired for. "Rugby, racing and beer" as generations of New Zealand men were told they were interested in.
There are issues around gender and gender roles that are changing for the better, Webb says - he thinks there's less casual homophobia and sexism in schools and in the culture at large - but there are issues that aren't: "The stuff about emotional repression in boys, I wouldn't be so confident that there's been any improvement.
"You still walk down any park on a Saturday and you'll still find dads yelling at their 10-year-old boys to get up and man up and act like a man when they've just fallen over and really hurt themselves.
"I wonder if that's getting any better and that's the serious stuff because if you don't learn those skills, if you're specifically trained to avoid those feelings, then you're going to be in trouble by the time you're a teenager and you're going to start causing trouble for yourself and other people if you can't recognise what's going on in your own head."
In an interview with Shortlist last year, Grayson Perry contrasted the thinking of traditional masculinity with feminism's forward-looking view of an equal world.
"Men are always looking back saying, 'Oh, the old days, when men were men. You'd cut your hand off and just wrap it up with a bit of Sellotape and then back to work.' And that was the ideal of men. We don't need that guy around any more; he sounds a bit of an idiot."
Robert Webb says: "There's nothing wrong with liking Top Gear if you like Top Gear and nothing wrong with liking football if you like football and I wouldn't pin the blame for any of this on any specific thing but it is part of the wider culture that is going, "this is what we ought to be interested in. And it's naive to think that we're interested in this stuff because we're interested in it. We're interested in it because we're also expected to be interested in it. And that's worth acknowledging."
How Not to be a Boy is not really about fatherhood, except insofar as dads are first boys and men, and whether or not they become decent versions of those things depends in large part on the lessons they learn from their own dads.
Robert Webb is a dad to two girls and, when asked what he hopes for for his daughters, he says: "I have the same ambition as any parent, which is to psychologically put them in a drawer called, 'Doing all right.' I just want them to explore their contradictory selves and do what they want to do without hurting anyone. That's it.
"I want them to have a good enough education that they feel they've got some options but I don't want to tell them they've got to go to this university or do this for a living. I want them to have the freedom to make up their own minds. I would say exactly the same if I had boys."
How Not to be a Boy by Robert Webb, Canongate, $33. Robert Webb is speaking to Andrew Dickens on Newstalk ZB, Sunday, September 3.