“When we started here, no one thought it was a good idea,” says Peter Murray, the director of Yorkshire Sculpture Park (YSP), as he sits in the cafe that overlooks the rolling 202-hectare (500-acre) estate that opened to the public in 1977.

Back then politicians weren’t interested, local residents and businesses didn’t understand it and the only people in favour seemed to be artists, says Murray. “In the early days there was the constant battling and fighting for funds. Then there’s the politics of the art world and the politics of regional and national government. We had to be incredibly strong willed and bloody minded.”

More than 40 years later the stubbornness appears to have paid off. The YSP is at the heart of Yorkshire Sculpture International (YSI), a new festival taking place across Leeds and Wakefield. There’s a Damien Hirst statue in the middle of Briggate, the main shopping street in Leeds. Down the road there’s new work by Rashid Johnson and Cauleen Smith.

Five Yorkshire-based sculptors are being supported throughout the 100-day event. The official line is that the Rhubarb Triangle has become the Sculpture Triangle with Leeds Art Gallery, the Henry Moore Institute and the award-winning the Hepworth Wakefield making this area of West Yorkshire arguably the best place in Europe to see sculpture.

Tau Lewis, 26, has her first exhibition in Europe at The Hepworth Wakefield as part of the festival. Photograph: Danny Lawson/PA

Murray is hopeful the event will help to further the area’s credentials as an arts mainstay. He uses the German city of Kassel as an example of a place transformed by hosting the Documenta international arts event. There was controversy in Kassel last year over Olu Oguibe’s 50ft (15-metre) obelisk, which the words “I was a stranger and you took me in” written on it in Turkish, Arabic, German, and English. The city was proposing to buy the sculpture to keep permanently, but there were protests by far-right politicians before it eventually returned to the city. In the febrile Brexit atmosphere any use of public space or money can become similarly politicised.

Brian Alexander is looking up at Huma Bhabha’s Receiver, a green and black humanoid figure that stands between the city’s county hall, its police headquarters and a statute of Queen Victoria. “If you want people from Wakefield to be onside, this is an old-fashioned mining community and this doesn’t wash,” he says. “This is the civic centre of the town and I think you need something more … civic.”

Huma Bhabha puts the finishing touches to Receiver 2019. Photograph: Sam Frost/The Guardian

Alexander shows me a Facebook exchange he had the night before with a young woman who said she was happy about YSI coming to the area. He disagreed with her and thinks the average Wakefield resident would question the need for the event when the city has lost £171m of council budget cuts over eight years. “People don’t have the right idea,” he says. “They’re saying ‘why has the council spent so much money on that? The money could be spent better on something we need more’.”

Funding for the festival comes in the form of a £750,000 grant from the Arts Council, which covers around half of the cost. The other half comes from partners including Wakefield council, 2023 Leeds, the University of Leeds and more than a dozen others.

You need to keep it international to keep people’s minds and imaginations open Simon Wallis

Godfrey Worsdale, the director of the Henry Moore Foundation, says there would be collective disappointment if fewer than a million visitors saw YSI, and he wants local residents to make up a large portion of attendees. “People in Yorkshire have got to be involved,” he says. “It needs to be internationally ambitious and locally relevant, and sculpture feels like something everyone can get around.”

For Simon Wallis, the director of the Hepworth Wakefield, the Brexit referendum result in the city – 66.4% of voters were in favour of leaving the EU – means his gallery has to play a bigger role in keeping the city outward facing. “When Nigel Farage came here people were over the moon, the turnout was incredible. It’s terrifying, it really is,” Wallis says.

A work by the US artist Jimmie Durham on show at the Hepworth Wakefield as part of the festival. Photograph: Danny Lawson/PA

“It makes me think that with this place we need to redouble our efforts and fuck the notion of coming up with lowest common denominator to please lots of people. You need to keep it international to keep people’s minds and imaginations open.”

Wallis’s uncompromising approach could be informed by the fact he has had to face and overcome pessimism before the Hepworth Wakefield opened in 2011. “I arrived in 2008 and the financial crash was happening and people were saying ‘no one will ever come’,” he says. “Now we have 250,000 visitors a year and a third of them are from the local area.”

Murray echoes Wallis’s sentiments about art – and sculpture in particular – being a potential force for change, reiterating that people now embrace the YSP after not understanding it initially. “Now 99% of people who come think it’s a good idea,” he says. “It takes time and if you’ve never had contemporary sculpture in the centre of Wakefield or the centre of Middlesbrough or Leeds, it makes people sit up. But art can be and should be provocative.”

Wallis sees a potential positive for the arts in West Yorkshire after the current political situation calms – a move to a more devolved system. “One of the good things that could come out of this is the notion of a devolution outside of London, and that these world class and challenging experiences could be there for everyone,” he says. “You don’t have to water something down just because it’s in the regions.”