During my years as a temporary New Yorker, it was my honour to befriend – and meet regularly for lunch – a Welshman who is among those rare people to qualify for that devalued and over-used term "genius": John Cale, known most commonly as the bass and viola player for the Velvet Underground, which is a shame, for he is the composer of so much more and better music since.

We met usually on Fridays, when his touring schedule and my deadlines permitted, at an excellent trattoria called Bar Pitti on the corner of 6th Avenue and Bleecker Street in Greenwich Village. Our conversations were a delight, as exhausting as they were relaxing because the subject matter hurtled between politics (Blair and Bush were at war), music, the random pointlessness of existence, weird nooks and crannies of history, literature and our daughters.

Some of Cale's favourite subjects – digital technology and espionage – left me bewildered. And I never knew he was interested in the obscurities of haute cuisine; there was no need to acknowledge such an issue in Bar Pitti, which was proof that nothing beats simple food – cucina casalinga (literally "housewives' cooking") – done well. He would nibble at salted spinach while I enjoyed farfalle ai funghi porcini. After decades of rock'n'roll excess, Venus in Furs, illness and injectable adventures, he was, and remains, a remarkably fit, teetotal 70-year-old. Crucially, however, he would attack the panna cotta smothered in chocolate sauce with as much relish as I did.

When he uprooted, 3,000 miles west to LA, and I moved the same distance in the opposite direction to London, we determined to remain in touch. We usually meet at Daunt Books on Holland Park Avenue, exchange gifts to read, then walk and talk in the park. And when we ate, it was invariably at Wagamama, to accommodate his need for soya and carrot juice. I drank Asian beer and found it hard to taste the food – so we found a compromise to suit us both: fantastic Lebanese mezze at a place called Al-Waha on Westbourne Grove. There was one especially memorable lunch there, for which Cale arrived with his manager Nita and daughter Eden, having just received his OBE from Prince Charles – he still wore the suit, and hair he had dyed pink for the occasion.

But now, for this article, Cale wants to try something more elaborate. Over in London to promote his new album Shifty Adventures in Nookie Wood, he opts for Dinner, Heston Blumenthal's restaurant at the Mandarin Oriental hotel in Knightsbridge.

For me, this is like boarding a space craft to some very weird planet. We sit by the window overlooking Hyde Park, and as ever we seem to continue the conversation we were having last time. "They've created an economy in America where people get rich in a certain way," he reflects. "It's a new kind of money with a new kind of power."

I get the impression, looking at our fellow diners and the businessmen drinking champagne in little corners with ladies to whom they may not be married, that we are the only people in here having this conversation.

The menu is made up of Olde Englishe dishes, with dates of their original debuts. Cale starts with nettle porridge (dating from 1660) made of "roast cod palate" which, the waiter explains, is a "cod's tongue cooked very slowly from the inside". Cale loves it. "This is delicious," he affirms, while I get to learn how big cods' tongues are – it includes their throats, and this one, the waiter says, has been cooked for 72 hours at 56 degrees.

As a vegetarian, I pose a difficulty, and start with a cold broth of lamb, without the lamb, and Cale is riveted by the fact that an egg floating about in it had been poached for several hours. He tells me about all this: it's called cryogenic or sous-vide cooking. He describes one machine which enables the chefs to "control the temperature of the water – a big thing with dials on it" while nitrogen is used to freeze.

I try to work out why Cale never talked about any of this before, and why he is so passionate about it now: this is test-tube cooking, the opposite of cucina casalinga in Bar Pitti. It may be because he loves gadgets that work well, and more important, because he approves of people who know what they are doing and do it well. Cale loves competence, and expertise.

While waiting for our main courses, we also discuss the new album, which is compelling and typically innovative. Cale likes silly jokes – he sends them constantly by email – and understands how they reflect the absurdity of life, which is why this record has a silly title.

He also remains strongly attached to his roots and childhood in South Wales. On such occasions as the premiere of an epic orchestration of his 1973 album Paris 1919 in Cardiff, or launching a UK tour in Wrexham, the crowds have loved his Welsh greetings – a man once leaned over me in the front row during a gig at the Cardiff Coal Exchange and affirmed at high, drunken volume: "He's ours."

And Cale loves experimentation with sound – this is his quintessence, and in this he can never stay still.

So on this new album we have a convergence of all these themes: surreal humour, connection to childhood and a soundscape that winds through thickets of lyricism to what Cale rightly calls, "the soundtrack to a claustrophobic film". Some of it is, he says, "about the trauma of childhood", the music full of mood swings but with "moments of shelter", as he puts it.

Perhaps that is why he likes this experimentation with food – it is technological.

His roast turbot now arrives. First cooked circa 1830, it is served with "cockle ketchup" and Cale gives the waiter quite a hard time over his account of how the dish was discovered by "some of the British emperors who went to Malaysia and saw the recipe" – which emperor? When and how did he or they go?

I have rice and flesh, with saffron but without the calf tail specified on the menu, which makes it a risotto alla milanese – which is almost as good as some of the un-cryogenically cooked versions I've eaten in Milan, and better than many.

At the end, something special happens. In the best tradition of his diet-busting panna cotta in New York, Cale insists on a dessert – something he had never done at Wagamama. And thank God he did, for along came a portion of brown bread ice cream and the recommended tipsy cake, pineapple-flavoured, roasted on a spit with apple juice and caramel, and doused in Marsala wine. "Non-ghee," Cale adds, "clarified butter" – then he gave up: "It's basically just a heavy dose of sugar."

It was also succulent, sweet and so good that Cale asked for another portion to go. He's spent too long in America – it was against the rules.

I suddenly remembered an uncle of my mother's in North Wales, who was Calvinist and avidly teetotal, but who always loved a second helping of potent sherry trifle with sabbath-day lunch after chapel. Maybe that was what Cale liked so much about tipsy cake, as he suddenly decides it is time to leave, springs out of his seat and walks out past the sheepishly secretive champagne-sipping couples.

Outside, by One Hyde Park, with its Ferrari showroom on the ground floor, we meet Cale's manager and the album promotion team. Had we had a good lunch? "Delicious, very good," says the satisfied musician, "did you?"

"Yes, thanks," replies the girl from the record label, "we went to the Lebanese."

Shifty Adventures in Nookie Wood is out now on Double Six/Domino Records