It is an unassuming object, a smallish, strangely glossy brown egg, and it is broken because of the carelessness of the last person you would expect – Charles Darwin.

"He squashed it into too small a box and it cracked, unfortunately," said curator Francesca Vanke, explaining the state of the spotted tinamou egg going on display at Norwich Castle Museum and Art Gallery.

The object is the only known surviving egg from Darwin's HMS Beagle voyage during the 1830s. Probably drawn to its glossy sheen, Darwin signed it C. Darwin and brought it back to Britain after collecting it in Uruguay.

The egg was discovered by a volunteer in the collections of the University Museum of Zoology in Cambridge five years ago and goes on display in Norwich as part of a summer art show exploring the cultural impact of birds.

"It is a coup," said Vanke, "but we have lots of coups."

Around 220 items are on display, including works by major artists integrated with taxidermy from the museum's collections.

The gallery is particularly pleased to have on display Holbein's A Lady with a Squirrel and a Starling, on loan from the National Gallery, because the sitter was recently identified as Lady Anne Lovell, whose family owned a house in East Harling, Norfolk. Other highlights include a John James Audubon oil painting, Hawk Pouncing on Partridges, Picasso's 1949 Dove and a beautiful 4,000-year-old Babylonian stone duck – "when you ask people how old do you think it is they say 1930s," said the show's other curator, David Waterhouse.

Vanke is the keeper of art while Waterhouse is curator of natural history, responsible for the dozens of stuffed birds in the show, everything from an Andean condor to a tiny hummingbird.

He said there were 20,000 in the Norwich collection. "Because so many are in store a lot of these haven't been on display for a hundred years, so this is a real opportunity to conserve them and get them in good enough condition for the next 100 years. It has been wonderful for me to get them out."

They include some poignant ones: a passenger pigeon, for instance, which used to be the most common bird on the planet – there were billions until hunting and habitat destruction led to their extinction, with the very the last one, Martha, expiring 100 years ago this year.

Another is a laughing owl from New Zealand, although Waterhouse said people had reported hearing its distinctive call in recent years. "There is a slim chance one might be alive – there is a glimmer of hope."

The same cannot be said for the rather chubby albino dodo painted around 1670 by the Dutch watercolourist Pieter Holsteyn. On loan from the Natural History Museum it is made from a stuffed version which was in the taxidermy collection of Rudolph of Prague and is on public display for the first time. "It is poignant, poor little thing," said Vanke. "There was not long to go for the species."

Waterhouse said dodos were essentially done for when pigs, black rats and cats were introduced to Mauritius and ebony trees were cut down. "It is never as simple as being hit on the head by sailors and that's the end of the species, and that is one of the messages of the show – we need to look holistically at habitats and conservation."

The exhibition examines many aspects of birds – how we have been fascinated by them and at the same time so terribly cruel towards them.

Being Norwich there are canaries in the show and there are also plenty of owls and parrots, to the delight of Waterhouse. "My PhD was in parrot relationships," he said.

The Wonder of Birds, Norwich Castle Museum and Art Gallery, 24 May to 14 September © Guardian News and Media 2014