Alison Lapper Pregnant, a 12-tonne marble sculpture of a disabled woman eight months pregnant by the artist Marc Quinn, was installed on the fourth plinth of Trafalgar Square 18 months after it was chosen from a shortlist of six artists.

A guest at yesterday's ceremony, Ms Lapper, 40, an artist, said she thought it was amazing, but not because it was her.

"It's inspirational. It puts disability and femininity and motherhood on the map," she said. "It's time to challenge people's perceptions about these things. I'm hopeful it can make a difference."

In a reference to the military heroes on the other plinths, she added: " At least I didn't get here by slaying people."

The unveiling was the culmination of a process that began seven years ago when the cook Prue Leith, as deputy chairman of the Royal Society of Arts (RSA), began a debate on what should happen to the plinth. It was designed in 1841 to display an equestrian statue, but insufficient funds for the project meant it lay empty for a century and a half. Thanks to Ms Leith, the RSA installed three temporary sculptures, prompting the Government to set up a committee to ponder its future. It was recommended that the plinth should be used for an ongoing series of temporary works of art, and the mission fell to Ken Livingstone when he became Mayor of London.

He was triumphant yesterday as the 12ft sculpture, carved in white marble from Quinn's cast in Pietrasanta, Italy, took its place at last. "When we launched this project, it was either ignored or the reaction was hostile. Now everyone thinks it's great," he said. "This is a work about courage, beauty and defiance, which represents all that is best about our great city. Alison Lapper Pregnant is a modern heroine - strong, formidable and full of hope."

The statue will remain in Trafalgar Square for 18 months, followed in April 2007 by Thomas Schutte's Hotel for the Birds, another work from the shortlist.

Alison Lapper Pregnant will then be available for sale at a price of £500,000 in an edition of three. Funding of £180,000 from the mayor and the Arts Council of England, which underwrote the project, will be reimbursed by the sale. But Quinn hoped that at least one would be bought for permanent display. "It's a public sculpture, I'd like it to stay public," he said.

His original inspiration was seeing old sculptures in the British Museum and deciding that if a real person with similar missing limbs walked in, museum visitors would be horrified.

"I realised there was no positive representation of disability in the history of public art," he said. But it was not a straightforward " message piece of art," he added. "To me, art is when you create space where meaning can occur."

Reaction

Sandy Nairne, director of the National Portrait Gallery and chair of the Fourth Plinth Commissioning Group

"We've got an even greater sculpture than I expected. The transfer from maquette to sculpture is a step-change not just in terms of scale but in the fineness of the carving and the fineness of the proportions. It's an important piece because it's both about ideas and about a person. It can provoke thought about Trafalgar Square, about history, but it's also about this extraordinary and fascinating person, Alison Lapper. I hope it improves the quality of the debate about contemporary public art."

Obinna Onyekwena, 27, MSc student of public health in London

"We've just arrived from Nigeria yesterday for me to study and we saw it on the television this morning and said we had to come to see it. I like the fact that disabled people are represented, that despite her disability she is there. I can't wait to get a picture of it."

Louisa Buck, critic and 2005 Turner Prize judge

"The best public art has to focus debate and make people question how they look at art and why. Otherwise art just becomes part of the furniture - things like, that horrible phrase, 'the turd in the plaza' or that are just decorative. It's a great subject to have in this historical, phallic, male hero-dominated square."

Alan Yentob, BBC's director of drama, entertainment and CBBC

"I like it. What is interesting is there are a whole lot of issues that this raises, such as what are monuments for, what about public sculpture? It opens up a debate about what art is, and whether you like it or don't like it, that is a very interesting dialogue. Look at old Nelson up there, he's got his back to it. He clearly doesn't like being upstaged."

Penny Toyer, 42, a supermarket duty manager from Bournemouth

"I don't particularly like it. It's not very flattering, it's unfair on her. We saw a programme on TV about her and thought we would come to see it, but I don't think it's beautiful at all. I would have liked something a bit more feminine. You wouldn't know it was a lady, facially. But I think it's a good idea to change the statue every couple of years."

Stephen Green, national director Christian Voice

"We've got three plinths with military leaders and the only ones we have today are in the Ministry of Defence sacking people. So I think we should have [Alison Lapper] but it would have been better to do a statue of her with her kit on. It's a pity he had to do an indecent statue. She has her breasts and other bits hanging out. We need more modesty in our nation, not less."

Martin Maloney, artist who has exhibited in shows including Sensation

"The scale is perfect, it's very simple. I think it's hard to make a piece of public sculpture because there are so many distractions in the outside world, but I think he's really pulled it off. You feel it's beautiful against the sky but also confrontational. It also makes me think of all the other classical sculptures that don't have arms."

Mark Lawson, writer and broadcaster

"I had no sense of the scale of it. I hadn't imagined it would be that big. Marc Quinn has always drawn on the classical tradition in his art and he clearly has here. It's very noble. The crowd here seem to have backed it. There weren't as many people talking about it as there were talking about the cricket but people clearly were engaged in what should be there."

Peter Hull, disability sports development officer, 39, from Southampton who was born without legs and with short arms

"I've known Alison nearly 40 years. Everyone is different but her diversity stands out more. Whatever we look like, we can still be beautiful to someone. This celebrates the diversity of humans. On the other plinths are men of courage and she is courageous. The statue will make a difference."