The Victoria and Albert Museum is to open through the night for the first time in its history in an attempt to meet demand for its sell-out Alexander McQueen exhibition.

More than 345,000 people have visited the show, called Alexander McQueen: Savage Beauty, since it opened at the central London museum on March 14 with visitors coming from as far afield as Afghanistan, East Timor, El Salvador and Uzbekistan.

Alexander McQueen
Fashion designer Alexander McQueen died in 2010(Danny Moloshok/AP/PA)

The museum, which opened on its present site in South Kensington in 1857, will open through the night for the final two weekends of its run.

Its director Martin Roth said: “We knew that Savage Beauty would be very popular, but the response has been even greater than we imagined. It is an extraordinary exhibition and I urge anyone who has not yet visited, wherever they are in the world, to make a trip to the V&A to experience this very special show. It is not going on tour to other venues so our aim is to provide as many people as possible with the opportunity to see it by opening through the night for the last two weekends. This will be the first time we have opened the V&A around the clock and we certainly think it is an event worth getting out of bed for.”

Lady Gaga in McQueen
Lady Gaga in McQueen (Frank Augstein/AP)

Celebrity visitors to the show include Lady Gaga, Kanye West and Kim Kardashian West and Maria Sharapova.

The exhibition, which fills 10 rooms in the museum, is a celebration of the work of the man who left school at 16 but rose through the fashion industry to become one of the world’s leading designers.

The Victoria and Albert Museum in London
The V&A will stay open all night (Tim Ireland/PA)

McQueen, the son of a London taxi driver, was aged 40 when he killed himself the day before his mother’s funeral after struggling with depression.

The fashion house that bears his name remains hugely influential and the Duchess of Cambridge’s intricately decorated wedding dress was designed by Sarah Burton of Alexander McQueen.