Boxers, briefs, corsets, thermals, slips and bras – the contents of the nation’s smalls drawer will be spilled at Undressed: A Brief History of Underwear, the biggest exhibition of underwear ever to go on display, which opens on 16 April at the Victoria and Albert Museum in London.

Underwear worn by Kate Moss, Dita Von Teese and Queen Victoria’s mother will be among the exhibits. Visitors will also learn that women didn’t tend to wear drawers – or knickers in modern parlance – until around 1810.

Displayed thematically, some cases are dedicated to items designed for hygiene, while others show those created to keep their wearer warm, and others worn while pregnant.

The exhibition, sponsored by Agent Provocateur, also includes nightgowns from the 1930s and a rubber corset from House of Harlot made for the exhibition.

The V&A has been keen to escape any cliched ideas of a dusty old textile collection. Parallels between historical and modern garments are frequent. The S-Bend corset from the early 20th century – designed to accentuate the wearer’s bottom and tiny waist – is strikingly similar to the silhouette that reality TV star Kim Kardashian has made popular. The kind of waist trainer Kardashian uses is also displayed here.

The subject matter feels particularly relevant for fashion in 2016. Curator Edwina Ehrman said they began working on this exhibition at the end of 2014 “when the pyjama moment was happening” on the catwalks. ”I had a hunch we would get another underwear outerwear moment,” she said.

The Liza Bruce slip dress worn by Kate Moss in 1993 – and displayed here – has become a cult reference for fashion this season. The exhibition shows one of its historical precedents in a dress from 1875 with a corset style bodice.

A museum worker adjusts a contemporary corset by House of Harlot. Photograph: James Gourley/Rex/Shutterstock

The V&A show highlights the tension in the design of women’s underwear between function and allure. X-rays displayed next to a case of corsetry show the difference in a rib cage when a corset is unlaced and laced. It’s hard not to wince when looking at the latter.

Such suffering for silhouette continues. A corset designed by Mr Pearl to be worn by contemporary performance artist Dita Von Teese is arguably even more extreme: covered with sparkles, its 18in (46cm) waist is the smallest in the exhibition.

Men’s underwear is also explored beyond the obvious Y-fronts and boxers. “I wanted to make the point that it’s about men too,” said Ehrman. “We have a fantastic menswear community in London.” The exhibition opens with a two-piece men’s underwear outfit from the second half of the 18th century, and there’s also a waist belt for a groom on his wedding day from 1842, using an early version of elastic.

Undressed at the V&A, sponsored by Agent Provocateur and Revlon, is open from 16 April until 12 March 2017.