V&A Dundee, the spaceship-like £80m museum that was one of the highest-profile new cultural buildings of 2018, has been nominated for the UK’s most lucrative arts prize.

The Art Fund has revealed a shortlist of five nominees for the Museum of the Year prize, which is worth £100,000 to the winner.

Along with Dundee, the 2019 prize will be contested by HMS Caroline in Belfast, Nottingham Contemporary, Pitt Rivers Museum in Oxford and St Fagans National Museum of History in Cardiff.

Museums and galleries in the UK have been and continue to be particularly hard hit by national and local authority spending cuts, but Stephen Deuchar, the chair of the prize jury and director of the Art Fund, said it was “very heartening that despite the rather grim landscape there is this relentless ingenuity coming out of museums”.

The prize is given annually to a museum that has shown, in the view of judges, “exceptional imagination, innovation and achievement in the preceding year”.

V&A Dundee is the UK’s first design museum outside London. It was completed four years late and for more than twice the early budget figures, but opened last year to a general feeling of goodwill and optimism.

Kengo Kuma’s building on the Tay, described by the Guardian’s Oliver Wainwright as “part cliff face, part galleon … like a curious craft sailed in from another realm”, not only looks remarkable but is regarded as a considerable feat of engineering.

There is hope it may do for Dundee what Frank Gehry’s Guggenheim has done for Bilbao in Spain, and there are early causes for optimism. Last month it passed the milestone of 500,000 visitors six months ahead of target.

HMS Caroline is the last remaining British light cruiser ship from the first world war and the Royal Navy’s sole survivor from the Battle of Jutland. It opened as a museum last year after a £20m rescue and restoration project.

Nottingham Contemporary opened in 2009, one of a wave of transformative regional art galleries that opened before austerity set in. Organisers of the Art Fund prize said there were several “watershed moments” for the gallery last year, including a strong exhibition programme. New virtual reality tours and an increased focus on performance and education were also cited as factors for the nomination.

Oxford’s Pitt Rivers Museum, established in 1884, has one of the world’s most important collections of anthropology and archaeology. It is nominated after a year of innovative programmes that included asking questions about the collection’s colonial past, and working with refugees to reinterpret collections.

St Fagans, an open-air museum that tells a history of Welsh life, is Wales’s most popular visitor attraction. Last year it completed a £30m redevelopment to become Wales’s national museum of history, opening new galleries and workshop spaces.

The judging panel this year comprises the BBC journalist Brenda Emmanus, the artist David Batchelor, Bridget McConnell, the chief executive of Glasgow Life, and Bill Sherman, director of the Warburg Institute. They will visit each museum before deciding on a winner, to be announced at the Science Museum in London on 3 July.

Previous winners of the prize have included Tate St Ives last year, Yorkshire Sculpture Park in 2014 and the William Morris Gallery in Walthamstow in 2013.