He met Ann, the other party to this historic event, again, when he was last on tour here in 2006.
"I was pleased and proud that such a lovely and kind woman had been my first love. Thank you, Ann," he wrote.
Cleese is on the line while on holiday on the Caribbean resort island of Mustique.
It's a favourite spot. It was there in 2012 that he married his fourth wife, Jennifer Wade, a former model and jewellery designer who is 30 or so years younger than Cleese's innings of 76.
As Cleese talks about everything from his admiration of Kiwi cricket captain Brendon McCullum to the reasons for his autobiography and his upcoming New Zealand tour with fellow Python Eric Idle, Wade can be heard chuckling in the background.
Especially when Cleese mentions her own New Zealand connections — her globetrotting family spent a couple of years in Whangarei, where she attended the local Catholic girls' school.
His encounter with Ann wasn't the only formative experience Cleese had in 1964 New Zealand when he was touring as part of the Cambridge Circus, a troupe that included other soon-to-be stars of 1970s British comedy.
It's also where Cleese first saw himself on television, after the old New Zealand Broadcasting Corporation filmed a performance and invited the company to have a look. It was both alarming and instructive.
As he wrote: "I had had no clue how awkward and strange I looked, and I shuddered to think that West End audiences had nightly watched this weird apparition. First, when I spoke, I had such a stiff upper lip that I scarcely moved my mouth: I resembled a third-rate ventriloquist; then my hand and arm gestures were so cramped it looked as though my elbows were stapled to my hips; and, silliest of all, when I hurried across the stage, the lower half of me floated about like a hovercraft, while my top half swayed to and fro, giraffe-style. It was almost impossible to believe this 'thing' was me.
"But once I had got over the shock, it proved to be the most useful feedback I ever received. I immediately started working on all my movements: exaggerating and relaxing my lips when speaking, enlarging my gestures, and learning how to walk more conventionally."
And so began the screen career of Cleese the writer and performer, on television in Monty Python's Flying Circus for three ground-breaking seasons in the early 70s, before he quit, thinking the shows had started to repeat themselves.
Then came 12 classic episodes of Fawlty Towers, later in the decade. Then it was on to movies and a sideline in training videos and books.
Now Cleese is bringing Python back to where his screen career began, sort of. It's just him and Idle — Python's most musical member — coming to Auckland and Wellington in March.
No, it's not the full Monty — the gang did a 10-show reunion season at London's 20,000-capacity 02 Arena, then headed to Sydney for an encore.
The tour didn't come here, says Cleese, because Michael Palin didn't want to continue despite a big offer to head across the Tasman, and to tour the United States.
So Cleese suggested to Idle that they keep going on their own. They've taken their joint effort to parts of the United States already.
"I can say if you were a Python fan you will have a good evening. The audience is very friendly. They don't think, 'I can't stand those two. I am going to buy six tickets.' There is something real about the transaction between us and the audience — there is no technology getting in the way."
The original reason for the Monty Python reunion was to pay for £800,000 in legal fees in a case about producer royalties from the stage musical Spamalot.
It wasn't the first time Cleese had gone on stage to pay court-imposed debts. The last time he was in New Zealand was part of his Alimony tour to pay third wife Alyce Faye Eichelberger, who was awarded a £12.2 million settlement when the couple divorced in 2008 after 16 years of marriage.
So he's kept touring and writing because he's needed to.
"When you have paid 20 million you have a dent in your finances, to put it mildly, and I need money to live. I have never been very good at saving it and investing it and I give most of it away anyway, so I have to keep earning. Performing is a very nice way of doing it.
"If I had not had to pay that off, I probably wouldn't be doing so much performing. I'd probably be doing slightly eccentric things to slighter smaller audiences."
The book is both an entertaining account of his comedy career and a revealing act of self-analysis, one in which he blames his rocky relationships with women over the years on the difficult relationship he had with his mother growing up.
The book finishes with the formation of Python and a tribute to his chief writing partner in the the group, Graham Chapman, who died in 1989, and a flash forward to the reunion shows.
The impetus for the book — other than waiting for an advance big enough to make it worthwhile — came over lunch with Michael Caine, who had published his own autobiography in 2011. "He was telling me what a wonderful experience it was ... that you recapture parts of your life that you totally forgot. I thought to myself, 'What a nice thing to do'."
Cleese is happy with the end result, though sounds mildly miffed that some don't think the book is as funny as he does.
"When I read it now I am pleased with it. It's what I wanted to do. Sometimes you set out on a project and the project finishes up quite different from what you were trying to do. This one I am very satisfied with. In a year's time, when I can come to it fresh and I have forgotten about this one, I'll do another. In the meantime, I will do a bit of performing. The nice thing about my business is you don't have to retire if you can write. You can go on until the pen drops out of your hand."
"I think it does. I am the happiest now I have ever been. I think partly it's because when you get older you don't worry about things so much. The second thing is I have a really lovely wife this time after some misfires, and we laugh hugely together all the time. She's just wonderfully silly. We laugh like kids most of the time and I am sure that very important people would think we are very childish and ought to act our age."
Lowdown
Who: John Cleese and Eric Idle in Together Again At Last ... For The Very First Time
When and where: Civic Theatre, Auckland, on Wednesday, March 23; Michael Fowler Centre, Wellington, Monday, March 28
Also: Cleese's autobiography book So Anyway ... is out now.