At least 40 screens line the white-brick and plate-glass walls of Jellyfish Pictures’ industrial-style office near London’s Oval, but the space is strangely silent: the powerful computers they are hooked up to are all somewhere else.

“Lots of companies in computer graphics, visual effects, animation, you’d hear the hum of the machines,” says Phil Dobree, Jellyfish’s CEO. “This is virtual. It means we can take it almost anywhere.” And they might.

With 200 employees on four London sites, Jellyfish is a highly successful part of a hugely successful UK industry. Fuelled by Pinewood, Shepperton and Harry Potter, Britain has become a world-leading centre for movie visual effects, or VFX.

UK-based firms provide Oscar-winning VFX and computer graphics (CG) for blockbusters such as as Gravity and Interstellar. Jellyfish – a multiple Bafta winner – has done Star Wars Rogue One and The Last Jedi, plus countless TV dramas and docs.

But, says Dobree, if the industry is among the world’s very best it is because it “has easy access to the very best”. More than 30% of people working in the UK sector, including at Jellyfish, are EU nationals. Brexit could wreck that.

“We have EU animators, modellers, riggers, lighters, compositors, CG supervisors,” Dobree said. “All the key skill areas. From Spain, Italy, France; from junior to very senior. These people are difficult to train and extremely sought after.”

About half are contract workers. “Often, when you’re doing a short-term job – a commercial, a TV series – you need people for a month or two,” Dobree said. “Right now, we can fly them in pretty much the next day. So what happens after 2019?”

The same question is being asked across the UK’s booming creative industries, an unsung economic powerhouse encompassing everything from advertising to architecture, including music, film, TV, creative tech, video games and the visual and performing arts. It employs nearly 2 million people – 25% more than in 2011.

It is the fastest growing area of Britain’s economy, producing goods and services worth some £87bn a year – more than the UK’s car, life sciences, oil and gas and aerospace industries combined. Its exports reached £21.2bn in 2015, nearly 10% of the UK’s total and almost 45% more than five years earlier.

“We should be seen as either the most, or one of the most important, future-proof engines for growth in the UK economy,” says John Kampfner, the chief executive of the Creative Industries Federation. “But one of the key reasons we’re so successful is that Britain is so ... open. The question is: is that soluble in Brexit?”

Some 96% of the federation’s 1,000-plus members told a survey last year they did not want Britain to leave the EU. Their Brexit worries include maintaining access to vital EU grants that have financed countless, often small arts companies and co-funded major cultural venues.

With the EU by far its biggest market, creative firms are also concerned by more technical issues about being outside the single market and in new trade deals, such as effective standards, regulatory and legal frameworks, intellectual property and copyright, the free flow of data and the digital single market.

Kampfner said the sector’s biggest concern “pretty much revolves around talent and free movement. It’s about our access to the best people, the implications of any new immigration system for employment, freelancers, touring and festivals”.

The federation publishes a detailed report on the question on Thursday, in which it is expected to call for free, same-day movement for creatives, if necessary through the introduction of special creative visas. If there are new restrictions, they must be “incredibly easy to navigate”, said Kampfner.

More than 70% of UK creative firms employ EU nationals, and 60% use freelancers, the federation says. Around 47% of all creative workers in the sector are freelance and most do not earn big money – often far below the £30,000 to 35,000 salaries currently needed to qualify for a non-EU visa.

Any post-Brexit immigration regime aimed at deterring EU nationals and aligning the current system with rules for non-EU immigrants, such as that outlined in a leaked Home Office document last month, could prove catastrophic: some 57% of creative firms already report serious skills shortages, mainly due to shortcomings in the UK education system.

“But it’s not just the practicalities,” Kampfner added. “It’s atmospherics, too. It’s one thing to permit people to come and work in Britain, another to welcome them. Think of the brilliant young creative from, say, France, who comes here, does a bit of bar work to pay the rent, works his way up freelancing in his field, and five years later is a star ... They just won’t come. They’ll go to Berlin, or Paris, or Athens, or Lisbon. Anecdotally, numbers are already down.”

Free movement of EU labour, which the government seems determined to oppose, is a concern across all parts of the sector. “Companies must be able to continue to attract the very best talent, and make decisions based on artistic rationale and repertoire requirements rather than on sovereignty,” said Steven Roth, the executive director of Scottish Ballet.

Caroline Rush, the chief executive of the British Fashion Council, said at the opening of London Fashion Week last month that since the British education agenda could not support creativity in the way the industry needed “we need to welcome and support international talent to come to the UK”.

Bait Studio, a design and VFX company in Cardiff that has worked on the BBC’s Casualty and other dramas such as Decline and Fall, is currently hiring more than 20 extra staff for several months to work on a feature film. Most will come from the EU, said managing director Jon Rennie.

“Not because we make a point of hiring from outside the UK – we try to hire locally if we can,” Rennie said. “But we want to bring in absolutely the best possible people for the job, and we need to be able to do it fast or the work will go elsewhere.”

Peter Rogers, the company’s creative producer, said the industry “needs free movement to continue”. Despite its attachment to Wales, the business was ultimately highly mobile, both men said. They had already heard of rival VFX companies “hedging their bets” by exploring a move to Ireland.

Back at the Oval, Manuel Reyes, 36, a senior computer graphics supervisor at Jellyfish, agreed the situation was tricky. “Everyone’s worried. At work, we’re very reassured. But generally ... you feel more uncomfortable. You start looking at other openings. So yes, if there are more hurdles, we’ll go somewhere else.”

But without something as “close as possible to free movement” after Brexit, said his boss, Dobree, “Britain’s CG and VFX industry will simply move on.” And without fast access to talent, “the industry will die” in the UK.

“We’re smart, we’re flexible, we already face sky-high real estate and other costs. We’re here because the talent is here and if it isn’t we can bring it here. The bottom line is this: if the government doesn’t get this right, these films and shows will no longer be made in Britain.”