So why is he ending his political cartoonist's strike, and why legs? "In 1987, I decided this was a game we were playing. It was the time of the Big Bang in finance and it made me realise that our whole society was obsessed by the money motive, and it was bolstered by the Tory party. We needed to take the wind out of their sails by simply ignoring them. People kept writing about them, drawing them, photographing them, and they love it. I felt disillusioned by it."
Indeed, up to a point, he still does. On the train, Steadman had been reading Suzanne Moore's article in Friday's Independent when she accused the Commons of a fundamental staleness and greyness. He completely agreed. But?
But now it was important to vote, a last chance. "If we don't get them out this time, what do we do?" he asks. He could feel himself sliding away from it all again: "There's more to life than bloody politics ... I would never have any of them to dinner."
You will have gathered that Steadman is an unapologetic, unreconstructed socialist of the old school, an admirer of Michael Foot, Denis Healey and the welfare state. He is fuelled now, as he was when he savaged Nixon, by old-fashioned moral outrage, at the length of time it took to get the Bridgewater three out of their cells, at privatisations of water and rail, at politicians' lack of culture and hinterland, at the creation of "the underclass, which is totally in the cold, a new community in limbo".
In the New Statesman, he complained: "There's pornography in the madhouse, madness in the food chain, stupidity at the heart of government, intolerance in the streets, greed in our water supply and childhood is a dangerous option."
He found, he tells me, that Spitting Image and mainstream political satire was "paying lip service to the worse excesses of the government; they were making the unacceptable acceptable in our living rooms. It was a little too cosy. I wondered why I had ever started political cartooning in the first place." Hence, now, the refusal to do faces: however savage, however grotesque, his targets might be flattered.
Steadman first came to public attention through Private Eye, where Richard Ingrams used him widely, often asking him to create pastiches of other artists' work. After 10 years of that, and a marriage break-up, he decided it was time for a change and set out rather abruptly for America. It proved an inspired decision.
"Within a couple of days of arriving in New York, I got a phone call asking if I wanted to go to Kentucky to meet an ex-Hell's Angel who had shaved his head ... he wanted to go home and find his roots which were in Louisville."
The shaven one was, of course, Hunter Thompson: his partnership with Steadman, who was in a state of English shock at "the screaming lifestyle of America" was hugely fruitful to both. They careered around the US together, most famously following the 1972 Republican campaign from Miami. Thompson had never come across someone so genuinely horrified by American lifestyles and wanted to expose Steadman to more and more.
"We were a couple of mavericks, we hadn't got proper accreditation, we were pissed - we were forever in a terrible state. It was still part of the hangover of the Sixties."
For Steadman, Miami with Nixon was a spectacle of surreal horror, suffused by the imagery of the alligator swamps on which the city was built, and he eventually fled back to Britain, with a cheap plastic alligator in his pocket from an airport vending machine, which then became the dominant image for the American drawings. "I got butterflies in the stomach drawing Nixon," he says now. He and the original gonzo journalist remain in touch and still, from time to time, collaborate.
His art is still instantly recognisable, close in spirit to the satirical attacks that made him famous in the Seventies. The splattered, blobby lines of ink; the grotesque, ballooning bodies, the fascination with the internal anatomy and functions of powerful bodies. "Maybe a lot of drawing is anal - but not anal retentive. I go the other way." It is not hard to see what this gentle-seeming, gentle-voiced and profoundly ungentle artist means.
So the new drawings fuse the spirit of Gray's Anatomy with the surreal European tradition - there are livid flashes of Bosch in Steadman, as well as the lessons from Hogarth, and the German satirical tradition. He thinks that exposing the veins and muscles, the human carapace and processes, is the best way of debunking the arrogance of politics. "It shows that we are all flesh and blood and that no one has all the answers."
So the legs of John Major and Kenneth Clarke are to be followed by a "Three Graces" featuring the legs of Virginia Bottomley, Gillian Shephard and Ann Widdicombe: bad news for them, even though "you will never see a politician's face in my drawings again". He worries that "it might be hard to sustain politicians' legs as a good support system" and that he will end up "playing the game" again - become a cult, he jokes, for foot-fetishists.
I think not. These are drawings so furious it is difficult to speak of enjoying them. But there is a fury and freshness which comes as a necessary shock to the half-awake system. Steadman is back. Looking at his mournful smile and thick, hard-working fingers, I'm suddenly glad I am not a politician