It’s the museum that has explored the history of underwear, the death of the suit and the glamour of Italian fashion. Now the V&A is turning its attention to Cartier with an exhibition of more than 350 jewellery pieces including gobstopper-sized diamond rings and dazzling tiaras.

The exhibition charts the evolution of the French jeweller across fashion, design and craftsmanship since the turn of the 20th century. The V&A’s existing jewellery collection is one of its most visited galleries and the Cartier story is already proving popular. Tickets for the first six weeks of the show, which starts on Saturday, have sold out.

Helen Molesworth, who has co-curated the exhibition, said her team had worked with international museums, the royal collection and private collectors to secure a variety of pieces, some of which have never been displayed publicly before. These include a wafer-thin brooch adorned with dozens of diamonds that was made in 1910 and a black opal tiara previously worn by Mary Alice Cavendish, the Duchess of Devonshire.

Founded by Louis-François Cartier in 1847, by the early 20th century his three grandsons Louis, Pierre and Jacques Cartier had transformed a small family-run Parisian business into a global household name.

Much of the exhibition explores the relationship between the British royal family and the jeweller. King Edward VII called Cartier “the jeweller of kings and the king of jewellers,” issuing it with a royal warrant just two years after it opened its first London store in 1902.

The whimsical floral designs by the British artist Frederick Mew, who worked for Cartier from the late 1920s until his retirement in 1971, were favoured by the British royals. In 1953 Queen Elizabeth II commissioned Mews to create a brooch showcasing a rare 23.6-carat pink Williamson diamond, previously presented to her as a wedding gift. Mews’ preliminary sketches, which have never before been displayed, are shown alongside the finished brooch, which is on loan from the royal collection.

Molesworth says she also came across sketches in the V&A archive by Mews for an rare black pearl bracelet that she realised were in fact, the initial designs for a wristlet commissioned in 1953 by the Maharani of Baroda. The bracelet, on loan from a private collector, is considered one of the most valuable in the world.

Cartier’s fanbase today spans from royalty to Hollywood stars, with the jeweller’s Love bracelets, which are secured on the wrist with a tiny screwdriver, appearing on many aspirational shopping lists.

An engagement ring worn by Grace Kelly in High Society, which she received from Prince Rainier III of Monaco months earlier, is displayed next to a Tank wristwatch first owned by Jacqueline Kennedy and later acquired by Kim Kardashian.

Many of the rarest items on show came directly from clients, who commissioned Cartier to mount them. In 1933, the American heiress Barbara Hutton requested 27 marble-sized jade beads from Myanmar (then Burma) be mounted as a necklace. Cartier set them with a diamond clasp before later adding tiny rubies. There is also a necklace featuring seven tiers of yellow and white diamonds originally commissioned in 1928 by Bhupinder Singh, the Maharaja of Patiala. Other designs feature jewels sourced by the Cartier brothers, including emeralds from Columbia, sapphires from Sri Lanka and diamonds from India and South Africa. The history of colonialism and unethical supply chains they would have relied on is generally glossed over.

The final room is dedicated to tiaras dating from the 1900s to the present day. Molesworth says she expects some people to visit several times. “You could spend hours in each room. To see this collection of objects together is very unusual. It’s very special.”