Mr Greenaway had planned to realise a dream of Rome's great 16th-century builder Pope, Sixtus V, and turn the huge, near-circular piazza into a huge sundial, using the ancient Egyptian obelisk in the centre as the gnomon, whose moving shadow would indicate the time.
For several evenings this week, lights placed around the piazza would have created a speeded-up 'day', during which the history and character of the square were evoked by sound, music and effects such as shooting stars and fireworks. The spectacle, lasting 10 minutes, would have been repeated several times every evening as the public strolled by.
The project, called 'the Cosmology of Piazza del Popolo', was to have been a highlight of the current British modern arts festival, 'UK Today', promoted by the British Council and the City of Rome.
The piazza, which was originally a forest and then a vineyard, is reputedly the site of Nero's tomb. It was also the gateway by which Queen Cristina of Sweden entered Rome on her conversion to Catholicism. The Latin motto that greeted her is still visible, carved over the central arch: 'Felici fausto ingressui' ('For a happy and blessed entrance').
It was not a happy entrance for Greenaway. Instead he encountered a real-life version of his film Belly of an Architect, in which an architect tries to stage an exhibition in Rome and is defeated by the obtuse powers- that-be. 'It is really a case of life imitating art,' he said.
First, the superintendent for Rome's cultural heritage, Francesco Zurli, said no. The lamps that were to have been perched on the piazza's famous twin baroque churches were too heavy, he said. The place would have been full of cables. There were not enough emergency exits in case of a disaster. The project was 'nice, but not very original,' he said, and suggested dismissively that it be staged out in the suburbs.
Mr Greenaway found the objections 'rather absurd'. The lamps that were to have been used weighed only 7lb each, he pointed out. There would have been only three cables and they would have been strung high out of way. The piazza has 23 exits and entrances. 'As a long- time devotee of Rome's monuments I would never remotely have considered anything that could endanger them,' he said.
The cosmology is one of many cultural events planned for various historic sites in Rome - including a sports event scheduled in the Foro Italico, built by the Fascists as a sports arena - that have been banned this summer.
But the Mayor, Francesco Rutelli, a Green, and his left- wing council, which is struggling to revive the city after years of bad government and neglect, were furious.
They and other critics pointed out that the superintendent had had no objections to the square being used for big neo-Fascist election rallies, with huge platforms and loudspeakers, or for New Year's Eve merrymaking or as a carpark.
The mayor appealed to the Heritage Minister, Domenico Fisichella, a monarchist and ideologue of the new National Alliance coalition party, which is dominated by the neo-Fascists. But Mr Fisichella, who is on record as declaring that he has no interest 'in any contemporary art whose criteria have not stood the test of time' - said no.
'It is a political decision,' declared Gianni Borgna, the city alderman responsible for culture.
'The truth is that a conservative and anti-modernist caste is emerging,' said Chicco Testa, head of the electricity company that planned the effects with Greenaway.
Vittorio Sgarbi, art critic and right-wing president of the parliamentary culture commission, agreed that it was probably a 'political ban'. 'The piazzas were made to be used by the citizens,' he protested. .
Greenaway has left Rome, but the row rages on. The leader of the city's former Communist councillors, Goffredo Bettini, has announced that his party will raise the issue in parliament.
'There we will demand that the superintendent and the minister be made to account for their behaviour,' he said.