"Besides, this and washing dishes are the only things that I really know how to do."
For a notoriously slow worker, who has claimed it can take him years to complete a lyric, Cohen has suddenly become very prolific.
Following 2012's acclaimed interrogation of morality, Old Ideas, Cohen will release an extraordinary new album next week, Popular Problems. And he reveals that there is already another in the works, which he jokingly refers to as "Unpopular Solutions".
"I continually blacken pages and scribble away, so I always have a number of songs that are half-finished," he says, but ascribes the new ease of the recording process to his collaborator, producer Patrick Leonard, who has essentially taken over musical composition and arrangement.
"Between the two of us we had this catalytic influence on each other. I don't know how other writers do it, but I just have a sense of gratitude that you can bring anything to completion in this vale of tears."
Lyrics emerge in a spontaneous and revelatory fashion, going through many revisions before Cohen is satisfied that he can "get behind" their ideas.
"You kind of keep your tools sharp by working all the time. We are professionals. You can't wait for inspiration. I try to do it every day.
"When something good comes, you have to be prepared to polish it, carve it and chisel it, that's the work. But the actual intention, what you are really going to be writing about, that's going to come up from a really authentic place that is deep and over which you exercise no conscious control."
See Leonard Cohen pay Hallelujah in 2009
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When I ask if the sense of time running out also plays a part in the quickening, he nods. "Well put. I mean, you are on the other side of the hill and it's no time to tarry." Cohen turns 80 on Sunday, for which he has jokingly suggested that he might take up smoking again.
"I really liked smoking. And I think about it a lot. I'm thinking about it right now." It will probably be a quiet occasion. "One of the charitable realities of my family life is that we hardly celebrate holidays or birthdays or anniversaries, so everybody's kind of let off the hook. I think it will just go by like any other day." But then he adds, after a beat: "I may have a smoke."
I first met Cohen 22 years ago, promoting his album The Future, and the experience has always stayed with me - his gentle humility and gentlemanly poise, his openness and kindness to strangers, and his fantastic eloquence, wisdom and humour.
When he engages with you, he really engages, his eyes shining as they lock on to yours, his low, soft-spoken voice drawing you in as if in a conspiratorial huddle. The Future offered a near-apocalyptic vision of the world to come, and Popular Problems brings this rudely into the present.
"When I said: 'I've seen the future, brother, it is murder,' unfortunately, I think that vision has been realised."
But he quotes the final uplifting track on Popular Problems, You Got Me Singing. "The bulletin is: 'You got me singing even though the world is gone/ You got me thinking I'd like to carry on."'
Earlier, in a press conference at the Canadian High Commission, someone suggested this was evidence of hidden optimism. "Yeah, I'm a closet optimist," Cohen drily responded.
See Leonard Cohen play Suzanne at the Isle of Wight Festival in 1970:
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Popular Problems addresses civil strife, conflict between lovers, families and communities. Cohen is not quite ready to call it a political album.
"I've tried over the years to define a political position that no one can actually decipher," he jokes. "Of course it reflects the world that we live in. One picks up these things from the atmosphere."
Cohen's Jewish roots are explored in a gospel song, Born In Chains. "We all live lives that are tethered to the circumstances in which we find ourselves, so in a certain sense everyone is born in chains. There are moments of liberation and moments of captivity. Life seems to move between those two polarities." Although he has embraced Buddhism, he says of his Jewish identity: "I grew up in a very conservative, observant family, so it's not something I ever felt any distance from. It is essential to my own survival. Torah values are the ones that inform my life."
Yet, on an album about civil war, the conflicts of the Middle East loom large and one song, Nevermind, is given a strongly Arabic flavour as it compassionately investigates the effects of defeat, dispersal and division. "There comes a point, I think, as you get a little older, you feel that nothing represents you. You can see the value of many positions, even positions that are in savage conflict with one another. You can locate components on both sides that resonate within you."
On Old Ideas, Cohen sang of wanting to write "a manual for living with defeat". "I wish I could really come up with something 'cos we are all really living with defeat and failure and disappointment and bewilderment, these dark forces that modify our lives," he said at. "Everyone is engaged in a mighty struggle for self-respect, meaning and significance. The first step would be to recognise that your struggle and your suffering is the same as everyone else's. I think that's the beginning of a responsible life. Otherwise we are in a continual savage battle with each other with no possible solution, political, social or spiritual."
Cohen quotes a track from his new album, A Street, in which he conjures up the fallout from a romance divided by war. "When I say 'the party's over but I've landed on my feet / I'm standing on this corner where there used to be a street', I think that's probably the theme of the whole album. Yeah, the scene is blown up, but you just can't keep lamenting the fact. There is another position. You have to stand in that place where there used to be a street and conduct yourself as if there still is a street."
Popular Problems grapples with big issues of how we behave in our divided world. But can a song ever really offer solutions to political problems?
"Hmm," says Cohen, sagely. "I think the song itself is a kind of solution."
Hear a track off Popular Problems, Almost Like the Blues here:
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Leonard Cohen: Popular Problems (Columbia) is released next week
