‘I’ve certainly been in the business of being open and authentic of late,’ acknowledges Alan Cumming. Asked to do a two-week run at the Cafe Carlyle in New York, he wanted to create a whole new show that was both revealing and intense. ‘What I really like about singing in this form is how raw it can be and how bare you have to be to do it. I thought that if I was going to do another of these shows, I really wanted to go for it. I want to sing songs that really mean something to me, be a bit more vulnerable and authentic. I want it to be as personal and intimate as possible.’

His Edinburgh International Festival show, Alan Cumming Sings Sappy Songs, is a hedonistic, late-night cabaret of music and honest anecdotes. ‘I think of cabaret as a smorgasbord of emotions,’ he says. ‘I really love that you can be laughing your head off one minute and suddenly something happens and it’s really touching or moving. There are some hanky potential moments; for me as well actually, even now after doing it for so long. But it’s also hilarious: I tell a lot of funny stories.’

What’s happened to Cumming in recent years has helped provide plenty of new material for a personal performance. In 2010 he appeared on the BBC’s genealogy show Who Do You Think You Are?, where he traced his maternal grandfather who served as a motorbike dispatch rider during World War II. Cumming subsequently wrote Not My Father’s Son, a family memoir documenting the complex relationship with his abusive father and his own deep-seated questions about his parentage.

This new show has songs for both his father and grandfather. ‘It’s easier for me to present myself in the stories because I’m a storyteller, I’m Scottish and I’m used to doing funny stories and being open in that way. It’s been an interesting journey to do that with the songs.’

Audiences will be treated to a range of numbers: one from Scotland, one from France, a Noël Coward song, one Cumming wrote with his musical director Lance Horne for a condom commercial and hits by Annie Lennox, Katy Perry and Miley Cyrus. ‘Every song is in there because I connect to it in an emotional way and I feel that my singing brings something to it and lets you hear it differently. There is little point in me singing a song that everyone knows and is a nice song: why would you bother?’

This will be Cumming’s fourth decade performing at the Edinburgh Festival. It was 1984 when he made his debut as part of comedy double act Victor and Barry alongside drama-school buddy Forbes Masson. He doesn’t look back on any early performances with embarrassment, but sometimes can’t quite believe their gall. ‘In early Victor and Barry shows we would be on stage, not knowing what we were doing. We either wouldn’t have finished the show or I’d be playing a song on the piano thinking, “I’m not sure if I know all the chords to this”. In retrospect that was part of what made it special; that energy and the fact that we were at our best when just kind of winging it.’

A star of stage and screen, with ‘808 and a half’ performances of Cabaret and seven series of hit US drama The Good Wife under his belt, he’s a guaranteed venue sell-out now. But his debut Fringe was similar to the experiences of many a fresh-faced performer taking on Edinburgh in August. ‘That first year, I remember we did a show for no one; for like, a cat. I also remember the feeling (which I’m glad I found out about early on) where you’re walking along the street and you see this flyer, or now a magazine cover, with your face in the gutter and some footprint on your face, discarded. That never changes, no matter how successful you get.’

That cat must have given him a decent review as Cumming’s acting career flourished, taking him to London and New York, where he is now based. A political activist who was a prominent voice in Scotland’s independence campaign and recently starred in a Spike Lee-directed advert for Bernie Sanders, he passed his US citizenship test in 2008 so he could vote for Obama. But what is it like to live in a country where Donald Trump is a presidential candidate?

‘Urg. It’s so embarrassing. There are two reasons this has happened, I think. Number one: it has become apparent that people are so angry that we’ve had a black president. There is an added layer to it as there is economic racism in America because black people used to be their slaves and used to be in an economic position lower than them. Now they have a chance to let that rage out because someone is encouraging it and condoning it. Also, the standard of education in America is so poor. You have a lot of not very well-educated people who don’t analyse things, who are much more predisposed to be affected by horrible bigoted rhetoric like his. I think those two things are like the perfect storm. If ever there was a reason for Americans in general to understand that they’ve got to get their shit together, this is it. I’m going to be working hard when I get back to make sure it’s not him.’

Cumming has already had the displeasure of meeting Trump. ‘It was last year at the Saturday Night Live 40th anniversary party and I was invited because I had hosted it once. My husband Grant and I were sat next to Donald Trump in the audience. It was me, Grant, Donald Trump and his wife, and then across the aisle was Sarah Palin! I was like, “what the fuck; how did we end up in this corner?”’

In 2007, after an extended period away from the Scottish theatre, Cumming performed at his first Edinburgh International Festival, taking the title role in The Bacchae by the National Theatre of Scotland. ‘I loved that, it was really fun. It was also kind of intense as it was the first time I’d been on a Scottish stage in 16 years. Something crazy like that. I remember it was a really big thing: “Alan Cumming returns to the Scottish stage after 16 years”. So, of course there was a lot of pressure. Also, the play is about a man returning home wanting the respect of his family, so there were lots of layers. It really was great to be back.’

Not content to feature in just one of the capital’s festivals this summer, he’s also returning to the Edinburgh International Book Festival to launch his new book, You Gotta Get Bigger Dreams, a collection of showbiz anecdotes and personal photographs. Or, as he puts it, ‘I’m double dipping this year’.

Edinburgh is a special city for Cumming. ‘It’s really the first place I ever performed. I’m kind of loathe to say that Victor and Barry in 1984 was professional, but it was the first place where people paid money to come and see me and definitely where I look back as the place where I cut my teeth and learned about performing. I did a play at the Traverse in 1988 called The Conquest of the South Pole and that transferred to The Royal Court. That was a big deal for me, it was a big change in my life. There have been lots of things like that: the first feature film I did was at the Edinburgh International Film Festival. It’s really a big part of my life.’

Alan Cumming Sings Sappy Songs, The Hub, Castlehill, 0131 473 2000, 6–27 Aug, (not 10, 14 & 15, 22), 10.30pm, £30; Alan Cumming: True Life Misadventures, Charlotte Square Gardens, 0845 373 5888, 27 Aug, 6.45pm, £12 (£10).