The subject matter of Anish Kapoor’s latest exhibition may not seem immediately attractive to those of faint heart, still recovering from this week’s Game of Thrones. Torrents of blood flow on to giant canvasses; the stuff of life, death, dirt and shame splashing and dripping with an exuberance that suggests that one of our best-known sculptors has very much enjoyed a move to painting in oils.

It’s curious, this joyful undertone, because his intent could hardly be more serious, a stark warning against the politics of hate and separation which stain so much of the world today. Brexit is very much part of that: “Our obsession with purity is very much what Brexit has come to be about,” he says.

His starting point is menstrual blood, and the purification rituals of his dual heritage — the Judaism of his Iranian mother and the Hinduism of his Indian father.

The “ancient practice” of treating menstruating women as impure, different, and separate and the cleansing ritual that takes place in a mikveh, is, he says an act which “affects everything else, our points of view, our sense of who’s in the tribe and who isn’t.”

Treating menstruating women as impure is the beginning of tribal affiliation, he says. “The question we have to ask is whether that’s good for us? In the 21st century, it seems the world is going that way more and more and more, which is hugely dangerous, I believe. We need to do, in a way, the opposite.”

So, while the history of Western art is distinctly phallic, Kapoor focuses on the womb. His paintings conjure up organs and tubes, openings and interiors, too abstract to be gynaecological, but not for the squeamish either. The predominate colours are red and black, but there are pinks and orange, too, and in some a fiery yellow. Some evoke fear and shame, or hint at violence. They are, nonetheless, full of beauty.

Alongside the paintings are the sculptures . In the Lisson Gallery’s courtyard, there are two vast mirrors, inviting us to consider the world and ourselves from a different perspective.

Then there are two works — one outside and one in the gallery —in which vast pieces of stone are carved to give the impression of rectangular boxes, containing ovoid forms. One is carved from a monumental piece of Iranian pink onyx to resemble a bath — or mikveh, or vessel — containing two egg-shaped objects, a deeper pink than the rougher outside. The way that the hard stone evokes softness and the idea of being held, alongside other ideas of purification and cleansing, is memorable.

Standing by this work, introducing the exhibition, Kapoor ponders whether a man “can deal with women’s questions — is a man allowed to?”

Later, when we grab ten minutes to talk, we return to this question. “I’m deeply into political correctness, because to not be is too right wing an agenda.

“But this other question about whether a man is allowed to make women’s things… whether a white person is allowed to do a black person’s thing, or whether a black person is allowed to do a white person’s thing or a woman’s allowed to do whatever… give me a break!”

The idea of cultural appropriation is “rubbish” he says. “Each one of us can claim what enters our consciousness without regard to whether you’re allowed to do it or not. That’s the freedom that artists have to insist on, it’s one of the things that being an artist is about.”

I ask about the undercurrent of fun that accompanies the paintings, that reminded me just a little of the finger paintings that young children make. He laughs, “They are finger paintings! I use a stick but mostly my hands and my body.

“I feel that one of the things we are doing as artists, it’s serious play. And if it isn’t joyful and playful, it won’t go anywhere…

“I think artists can dare — even if we just fumble around — to go there. What is my interior, what is this space inside of me, why is this space inside of me so much bigger than me? All those existential questions — very simple questions at one level — they are, if you like, the working matter of this serious play.”

The tallest part of the exhibition towers above us, a vaguely Christmas-tree shaped heap of welded metallic shards. It looks angry, I say, and he agrees. “Very, very angry, unwilling to be resolved and full of connections. It’s ‘male’, and yet aspects hint at the female as well,” he says, indicating the spaces and voids and curves in the structure. Perhaps a genderquake future, where boundaries between male and female are increasingly blurred will affect his work, as gender differences change and blur.

His ideas about separation and its dangers are very much part of his Jewish identity. He is not a “practising Jew” he says, he never was, although his maternal grandfather was the chazen of shuls in India. But he is “hugely conscious of my Jewishness, it matters to me massively.”

Born in Mumbai in 1954, he moved to a kibbutz in Israel as a teenager, later studying electrical engineering. It was in Israel that he decided to be an artist, and moved to London to study, where he has lived ever since, becoming one of our most famous artists. Currently there's a retrospective of his work at Pitzhanger Manor in Ealing, and this is his seventeenth exhibition at the Lisson Gallery. He was knighted in 2013, a year after creating the 115m high tower in Stratford for the London Olympics, now an East London landmark which reminds us of that distant, sunny time.

Back to the Lisson Gallery, and his  warnings about boundaries extend to the Jewish community. He argues that patrilineal descent should be accepted. If we did that, he says, we could double the number of Jews in the world. Inclusivity is all. “Instead of who we exclude, why do we exclude them, and who decides? And is it a matter of the colour of your skin, the place you come from?”

Jews, he says, come in all sorts and that should be celebrated. And that includes anti-Zionist Jews, “because you can be anti-Zionist and pro-Palestinian and be very Jewish and not antisemitic.

“To conflate those things is a huge mistake."

“All the major writers of the left, from Marx onwards were Jewish,” he points out. In fact Judaism, with its emphasis on community is intrisically leftist. “I implore our Jewish sisters and brothers to not be taken in by the right-wing press…” Including the JC? “Yes!”

Our wish to protect ourselves, he says, should not go so far as to endanger us. “Really we have to get this in some perspective. These are all ways of isolating ourselves and we mustn’t do it.”

Anish Kapoor is at the Lisson Gallery May 15 to June 22.