Fans of Kylie Minogue often talk about her 30-year career in terms of chapters. There was the late-80s perm-pop era, post-Charlene from Neighbours; the dance-pop era; the hot pants-sporting disco era; a slightly less successful indie era; and last year’s country era. This summer, however, saw her gloriously combine them all during an emotional Sunday afternoon “legends” slot at Glastonbury, 14 years after she was forced to cancel a headline performance following a breast cancer diagnosis.

Woven throughout her career has been an old-school devotion to privacy: we know the Kylie she’s keen to present, but perhaps not the real one. If anyone can get her to open up a bit, though, it’s Alan Carr, with the pair showcasing their decade-long friendship for Christmas Day’s Channel 4 special. Titled Kylie’s Secret Night, it sees the enduring pop icon surprise a handful of super-fans with performances, chat and even a comedy skit in which she at one point says: “Spank me harder, harder!” in the back of a taxi.

This afternoon, ensconced in the corner of a fancy central London hotel and giddy on Christmas and high-grade tea, the pair muse on Glastonbury, passionate fans and, most crucially of all, the strength of sticky tape.

I have a barbecue and a roast on Christmas Day Kylie Minogue

Alan Carr So Kylie, what are your Christmas plans?

Kylie Minogue Just having some family time. Usually I’m in Australia.

AC Whenever I get asked this, people think I’m being elusive, but I work hard all year and I just have a lock-in. I just wear a onesie for three days and drink red wine, and my lovely husband waits on me hand and foot. Do you know what I watched last year? I’m so embarrassed ... The Meg.

KM I’ve never heard of it! I go for Elf. Maybe The Muppet Christmas Carol. The Sound of Music. Love Actually. And – can I say? – I love wrapping presents.

AC This isn’t going to stay in the interview, obviously, but do you find the quality of sticky tape has gone down over the years? It doesn’t stick any more!

KM Because it’s Magic Tape, and that’s not good for wrapping presents. You know, the one that’s a bit opaque.

AC Well, there’s your headline for this. “I’ve been using the wrong Sellotape for years”: Kylie exclusive. Maybe we should all just use tit tape! It’s never let me down. Do you eat turkey? Do you have a barbecue on Christmas Day?

KM We have both. So you have the barbie going, because it’s usually boiling, but we’ll probably have an honorary roast, because you have to. But we don’t do what we did when we were kids, where all the cards were snowy and you’d put the snow on the windows and the tree had fake snow, but it’s 35-40 degrees outside! For New Year’s Eve I don’t mind working, because you don’t have the pressure. One year, I was home alone. I just watched TV, and it was bliss. Well, I mean, I didn’t have a boyfriend, I didn’t have any family here, but I really enjoyed it.

AC Oh, Kylie, I’ve got a spare room! Ring me, we’ll have a lock-in together. I want to ask you this: at parties, do you put Kylie songs on?

KM No! I don’t do that. Someone else might. If they do, I just have to roll with it, I suppose. Depends how many rosés I’ve had at that point.

Kylie Minogue and Nick Cave on the Pyramid Stage, Glastonbury 2019. Photograph: Samir Hussein/WireImage

KM So have you been to Glastonbury, Alan?

AC I have. I had a bit of a midlife crisis before I turned 40 and I thought: What haven’t I done? Everyone said: “Go to Glastonbury!” So I went, and it was the muddiest it’s ever been.

KM I’m never going with you!

AC No, don’t. You see those Instagram people and they’ve got the wellies and the cut-off shorts. Well, I had a footprint on my hat and red wine down my top … It was only 9am. You didn’t go out and about at Glastonbury, did you, Kylie?

KM No, no. I’d only been once before, which was a fly-in and fly-out situation with the Scissor Sisters. So just [playing] one number. Now I get it: you’ve got to call up your friends when you do that kind of thing, which I ended up doing with Chris [Martin] and Nick [Cave]. In a way, I still haven’t had the Glastonbury experience of being there overnight, roaming around, seeing everything. I still feel like I have to do it, as a rite of passage. I’ll probably be more like your picture; I don’t think I’ll be able to manage it like the cool girls. In fact, maybe I’ll retract my former statement: I should go with you and we can get real sloshy together.

AC Next year, they’ve got Diana Ross in the legends slot. But she’s got such a hard act to follow.

KM [Looks coy] Thank you. People ask me about [my 2019 performance] all the time, and I wish I had a neat little tagline, but a portion of it is a blur. I’d have to watch it again to really go: “Oh yeah, we did that,” or, “We stuffed that bit up,” or, “That was good.” It’s sensory overload. I had all the build-up, the panic, and I couldn’t even say the word [Glastonbury]. We just called it the Short Show, because the rest of the summer shows were 90 minutes and we had to make [this one] 75 minutes. I had everyone going: “You can’t go over,” except for Chris Martin saying, “Do whatever you want!” Then I had to think about how I was going to address “it”: me being there when I had to cancel so long ago.

AC Had you ever played to that many people before?

KM I’d never seen that many people. I’ve seen some shots from behind me to the crowd and it’s no wonder I can’t compute it!

AC I’m being really shallow now, but do you get a goodie bag for doing Glastonbury?

KM Actually, I don’t think I did. I wish I’d bought some more merch; I have one T-shirt and one tea towel. That’s it. The tea towel will not be used, even though I love souvenir tea towels. They did make a cake for me, which I didn’t know about until afterwards. When I got backstage there was this fairly sizeable pyramid cake. To this day, I don’t know who made it. There was a little miniature me on it, and apparently Emily [Eavis] or Stella McCartney was like: “Get rid of that, she can’t see it!” [Laughs] It wasn’t quite lifelike. Bless whoever made it, though. They really put their heart into it.

Kylie’s Secret Night, with Alan Carr. Photograph: Ray Burmiston

AC Speaking of merch, in the TV show, we went to this guy called Vincent’s house. He’s an uber-fan and he had a Charlene jigsaw! And then there was a guy covered in tattoos …

KM Really beautiful ones.

AC … of every era. He’d even changed his name by deed poll to Minogue.

KM David Minogue.

In Neighbours as Charlene Robinson. Photograph: Fremantle Media/Rex

AC It would make a cracking episode of Who Do You Think You Are? This one branch of the family tree going all over the place.

KM I think he might have been the … I don’t want to say weirdest but the most confronting: “You’ve changed your name!?” Lots of really touching stories.

AC When you came onstage, obviously it was a big surprise. There were people crying. The love for you in the room!

KM Even after 17 hours of filming in 55 degrees.

AC We did have a little break, which was nice.

KM Two and half hours after it started! I was having a hyperglycemic low, but I got through it. It was a celebration but also forward-looking. We are not just celebrating something that finished 20 years ago. This year, with Glastonbury, with this TV show, it’s marking this point in time, but what’s great is what’s happening next. I’m really jazzed about [the music] to come. I think it’s going to be getting back on the dancefloor, like grown-up disco; that’s where I want it to be. Shimmery.

AC In the final part of the show, we voted on the best Kylie single, and if you thought Brexit polarised Britain, you should ask people about their best Kylie song. We nearly had riot police. It was like: “SPINNING AROUND!”, “BETTER THE DEVIL …!”, “DANCING!” There’s a lot of love – and even some anger.

AC You’re a gay icon, Kylie, but I feel you’re more than that. You’re an icon.

KM Thank you. That helps me, because when I’m asked [what makes me a gay icon], I don’t think I’m meant to know the answer to that question.

AC If you knew the answer, you’d disappear up your very pert bottom.

KM Being able to look out at my shows for years and years now, everyone’s represented there. Long before our new inclusive society, which is fantastic, my shows have pretty much always been like that.

AC Camp gets thrown around a lot, to me especially but, you know, it’s said like it’s a bad thing, but there’s nothing wrong with being camp. With you, the hits come every album, and you just give people what they want. Every time there’s something different.

KM People have also seen me not get it right.

AC You’re not talking about the Charlene perm, are you?

KM It wasn’t a perm!

AC It was your real hair!?

KM Yes, I’d just use a diffuser and I’d scrunch it up with mousse. [Laughs] And now I just flatten it out and clip it in.

AC When did you get it wrong?

KM Babe. Plenty of times. I just don’t think you can get it right all the time, but you’ve got to keep doing it to have a chance.

Kylie’s Secret Night, Christmas Day, 10.30pm, Channel 4