Ideas that didn't find a platform

Tracey Emin, Anish Kapoor and Sarah Lucas are among those who failed to get on the Fourth Plinth in Trafalgar Square. Charlotte Cripps finds out what we missed – and how big-name artists cope with rejection

How does a famous artist deal with rejection? Those who have had their proposals for the coveted Fourth Plinth spot in London's Trafalgar Square turned down include Tracey Emin, Anish Kapoor, Sarah Lucas, Bob and Roberta Smith and Jeremy Deller. A new exhibition, Fourth Plinth: Contemporary Monument, which opens at London's ICA next month, is the first time all the designs including maquettes and archival material have come together – including for those works that didn't make it on to the plinth.

Emin's meerkat sculptures Something for the Future were not given the green light – but although she is not used to being rejected, she took a big sigh of relief when it was turned down. "I loved working on the Fourth Plinth project. My original idea was very simple – just a small tiny sparrow on the edge of the plinth. I should have stuck to that really," says Emin. "But I somehow got carried away and brought the meerkats in en masse. A little animal I have loved since childhood – along with the rest of the nation. But as much I loved them and loved doing the proposal, my relief in not getting the commission was a million times greater. From Bed to the meerkat – not the way I want to go!"

Other artists who didn't make the grade include Sarah Lucas with her proposal, This One's for the Pigeons – of a red car with pigeon droppings all over it. "For me, Trafalgar Square always meant pigeons. I was one of the children who purchased a tub of bird seed whenever I was passing through and stood with my arms out as they fluttered around me," says Lucas. "I'd take the 29 bus home from right in front of the National Gallery. Thinking about the shit Routemaster might be more apt – but no more likely to get chosen."

Deller's Spoils of War (Memorial for an Unknown Civilian) of a vehicle destroyed by a truck bomb in Baghdad in 2007 was not picked for the Fourth Plinth either, but it was not a wasted endeavour. It still toured around America and is now installed at the Imperial War Museum North. "To be asked to submit an idea for the Fourth Plinth is an invitation to be irresponsible, outrageous and absurd sometimes at the same time; it's perfect," says Deller, who was invited to join the Fourth Plinth Commissioning Group this year, five years after his submission was rejected. "I wasn't surprised my car was rejected because it was quite a provocative and controversial idea," he says. "You mustn't take these things personally but understand there will be other opportunities." Why do some works make it and others get rejected? "Because they are better ideas and are more practical in the public theatre," says Deller.

Kapoor's Sky Plinth featuring large concave mirrors attached to the plinth facing upwards to reflect the clouds as they pass was also left on the rejection pile. So too was Bob and Roberta Smith's (aka Patrick Brill) 2008 effort, a 100ft illuminated peace sign Faites L'Art Pas La Guerre ("Make art, not war"), powered by the sun and wind; it ultimately lost out to winner Antony Gormley who got members of the public to spend an hour each on the plinth. "The Fourth Plinth is unique in offering London a Turner Prize-style public art competition," says Smith. "Art looks constrained in white spaces and artists increasingly want to talk directly to the public. I am only sad I did not win, but it was fun trying."

While Gormley, Rachel Whiteread, Marc Quinn and Yinka Shonibare have had winning proposals, the first was Mark Wallinger's sculpture of Christ, Ecce Homo, in 1999, after the plinth had been empty for 100 years. Is it tough choosing the right proposal? The Fourth Plinth programme is led by the Mayor's culture team, under the guidance of the Fourth Plinth Commissioning Group (FPCG) with an eclectic panel of 10 special advisers including Deller; Grayson Perry; Matthew Slotover, the co-director of Frieze; Tamsin Dillon, head of Art on the Underground; presenter Jon Snow; writer and broadcaster Ekow Eshun; Iwona Blazwick, director of the Whitechapel Gallery and Justine Simons, Project Director at the GLA .

Do artists get upset when their work is rejected? "Artists put a lot into their proposals and the shortlisting of the final six works is a public process so it's hard for anyone in that position not to take it a bit personally," says Eshun, who is also the chair of the panel. "Every decision is difficult. We're debating up until the very last minute."

Snow, who is better known for presenting Channel 4 news, says the panel have never come to fist fights over a final decision. "Artists put forward amazing ideas but a main concern is whether the proposal is do-able," says Snow. "Bob and Roberta Smith's peace sign was designed to be about the height of Nelson's Column – but the debate was about whether it could be done, not if we liked it."

The Fourth Plinth brief is "quite open" says panellist Simons. "We ask artists to think about the plinth and the context of Trafalgar Square as well as a few practical things, as it has to survive the elements for around 18 months," she says. "The challenge of the plinth is to have a great idea. It's not as easy as it looks."

Fourth Plinth: Contemporary Monument is on 5 December to 20 January 2013 at ICA, London SW1 (