Unless someone has unearthed a vinyl record entitled "Bah–Bah-Baaah-Bah-Bar-bara Hepworth," Emily Young is surely the only British stone sculptor to have a classic Sixties pop song named after her.

It was "See Emily Play" by Pink Floyd, a whimsical piece of early psychedelia written by the band's co-founder Syd Barrett. Emily Young was 15 when she met the druggy and doomed Barrett at the London Free School in 1965. "I used to go there because there were a lot of Beat philosophers and poets around," she says. "There were fundraising concerts with The Pink Floyd Sound, as they were then called. I was more keen on poets than rockers. I was educating myself. I was a seeker. I wanted to meet everyone and take every drug."

What were her impressions of Syd? "He was absolutely delicious. He was a natural poet and artist, a creature of the forest, like Puck in A Midsummer Night's Dream. He was going through hell at the time because he was taking far too much acid and he knew he was in danger."

Did she ever snog him? There was a silence. "As I said," murmured Emily, "he was delicious."

It's pleasing to reflect that the one-time teenage muse to a rock star should spend a successful career bringing out the soul of actual rocks. After years of being feted as "Britain's foremost female stone sculptor," she recently lost the F-word when the art critic of the Financial Times called her "Britain's greatest living stone sculptor." It's a little hard to imagine this short, extremely handsome, rather regal woman with black hair and sparkling blue eyes taking a hammer and chisel to a lump of granite. Her works are instantly recognisable and accessible. She deals in spectacular lumps of stone – quartzite, onyx, marble, alabaster – to which she gives an identity by carving a face but leaving the remainder of the rock displayed in its raw, craggy intensity, as if the face had grown or evolved organically.

"I'm not like 97 per cent of stone carvers," she says. "They'll choose a stone to fulfil a preconfigured design, make drawings and a maquette, and sell the idea to a family, or an army or a business who'll pay for it to be made, usually glorifying a person or a battle. What I do is, I go to the quarry and see these pieces sitting there, beautiful objects in themselves. And I'm trying to say to the viewer, 'LOOK AT THIS STONE, IT'S YOUR ANCESTOR.'"

Her new exhibition is called We Are Stone's Children. The overused word "awesome" enters your mind as you inspect the 10 stone heads on display: the neoclassical serenity of Dark Forest Head 1 & 2, carved from Dolomites limestone, the faces held in "ancient, dreamless, uninvaded sleep" like the Tollund Man in the turf of pre-history. Red Mountain Head, by contrast, is the face of a warrior, emerging from a fire of wild red, orange, brown and white stone that the carver has left raw and untamed.

"I've been trying to tell a truth about the origins of human life and consciousness," she says. "I'm studying the origins of life in stone – our little Big Bang, four and a half billion years ago, when we started off as dust, floating around the sun. The whole of life on earth is inside our own bodies, and stone is the solid record of the history of the earth. We're both embodiments of the history of the world."

Young talks a lot in this vein, in her cut-glass, English-rose delivery. She explains how stones aren't inanimate, but have electromagnetic forces inside them. She talks about the need for humans to stop and contemplate the universe. About angels and Gaia and "deep ecology" and how the qualities of Greek gods have counterparts in human hormones. You might be tempted to discount it as earth-mother mysticism, but she won't have it. "There's nothing mystical about our relationship with stone," she says severely. "It may be mysterious, but it's absolutely basic. I put how I feel while I'm carving into the stone, and bring out a little relationship between the stone and the person looking at it."

She finds the stone in Italian quarries. "I'll buy 20 pieces at a time because they wave at me, saying, 'Hey, I'm really beautiful,' or 'I've got lots of moss growing on me and nobody knows what's inside me.'" She transports the chosen ones to her studio in Santa Croce, Tuscany. "It's a half-ruined hillside convent, very old and only partly habitable." And there she pitches in with hammers, chisels and power tools: angle-grinders, sand-blasters, compressed-air drills to cut through stone, and smaller, dentist's-surgery-size ones for more delicate work. She has written about this unwonted physicality as if it were something close to meditation. "I try to find a place where I can be still in myself, and embrace it and say, this is what humans are – what do we have to be, to stop focusing all our desires on instant gratification, and become more conscious of how we run our societies?"

Young has a remarkable pedigree as an artist: her grandmother Kathleen Scott was a sculptor and a pupil of Rodin who later married Robert Falcon Scott, he Of The Antarctic. Did Emily know her? "No, she died too young. But she wasn't a sculptor, she was a modeller in clay. She was on the team Rodin had around him. But he was mostly a modeller too. If he wanted something done in stone, he'd have someone carve it for him." She's scathing about modern YBAs (like Marc Quinn) who design artworks for others to carve. "He's no more a carver," she says, "than I'm Napoleon's boot-boy".

Her mother remarried Wayland Young, 2nd Baron Kennet, and Emily grew up, one of six siblings, in London's Bayswater. Her education was sketchy – one term at Chelsea School of Art, followed by a period at St Martins – but she developed her ideas about art while travelling, in the 1960s and '70s, through India, Pakistan, Africa and the Middle East. "I was very young and I saw wild nature – getting lost in the Himalayas and the Hindu Kush and Afghanistan. When the rains came, you had to stay until the waters died down. It was so beautiful, so wild, and man had no place there, although there were people living in tiny valleys with some goats. But everywhere I went, there was art. And it wasn't Western art. It was human art."

So Young because a kind of mediator between humanity and nature in its most primitive geological form. Her astonishing heads have faces born from the rock but carved and burnished to a point of exquisite sophistication. If she were given the fourth plinth in Trafalgar Square to fill, what would she put on it?

"Probably I'd put one of the great big heads, very sombre. A little piece of quietness in the middle of the hurly-burly. A reminder to people to stop and think just for a second."