A complaint has been lodged after a man stood naked on a Trafalgar Square plinth as part of the ongoing One and Other art installation.
Justin Holwell stripped and posed naked on the fourth plinth during his one-hour slot from 1400 BST on Sunday.
Ex-detective Mark Williams-Thomas said his wife and children were "annoyed and upset". He complained to police but Mr Holwell was not taken off the plinth.
A police spokesman said it was not a crime to appear naked in public.
Artist Antony Gormley's One and Other project enables public volunteers to stand on the central London square's fourth plinth for one hour at a time.
They are allowed to do anything during that time, as long as it is not illegal.
Mr Holwell, 24, from Loughborough in Leicestershire, said he confirmed with event producer Artichoke that he would be permitted to undress while on the plinth.
Afterwards he said: "I was chatting to my mates about it; they see me as a bit of an exhibitionist, this seemed the natural way to go."
Mr Holwell, who works in a double-glazing factory, added: "It's the human form, everyone's the same, it's not like I'm showing off something that no one else has got."
But Mr Williams-Thomas, a former Surrey Police detective constable, said his three children, aged between eight and 13 years old, were "very shocked and embarrassed" by Mr Holwell's nudity.
This was a public place and therefore I should be able to take my children without the fear of them having a man naked exposing himself
He approached nearby police officers and asked them to intervene. However, after contacting a superintendent, the officers said they would not take any action against Mr Holwell.
Mr Williams-Thomas subsequently complained to the Metropolitan Police.
Mr Williams-Thomas said: "I fully expected that the surrounding police or organisers would stop this man. To my total surprise they stood by and did nothing."
He added: "This was a public place and therefore I should be able to take my children without the fear of them having a man naked exposing himself."
Mr Williams-Thomas said Mr Holwell committed an offence under common law by exposing himself.
But a Metropolitan Police spokesman said: "We can confirm officers have received a complaint with regard to an exhibition on the fourth plinth on Sunday 30 August.
"This complaint is currently being considered, and the complainant will be notified in due course. Any complaints are considered on a case-by-case basis."
Event producer Artichoke said a number of participants have chosen to remove their clothes.
A spokeswoman said: "We have been working with the Metropolitan Police for several months and they agree that there is nothing illegal in nudity, provided no obscenity is committed, which is why they did not intervene in this case."
Earlier last month police ordered a One and Other participant to put his underpants back on after he appeared naked on the plinth.
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