If you’d been outside the luxurious Chateau Marmont hotel in Los Angeles in the early hours of Monday 23 September, you’d have seen Phoebe Waller-Bridge reclining in a chair, cigarette in one hand and cocktail in the other, surrounded by her many Emmy awards, enjoying her position in the vanguard of an increasingly dominant British television industry.

The following day the British television industry lost control of the star they had created. Amazon Video announced they had signed an exclusive three-year deal with Waller-Bridge – speculated to be worth as much as $20m a year – to produce programmes which will launch exclusively on the internet giant’s platform.

Josh Cole (@JoshCole8) All hail the queen 👑 #Fleabag #Emmys2019 pic.twitter.com/TFkMvQRAXt

There is a nationwide shortage of British studio space and support staff, as companies flock to the UK to take advantage of local talent and favourable tax incentives. There is also enormous demand from US streaming companies for big-name British talent – ranging from Waller-Bridge to The Crown’s Peter Morgan and even David Attenborough – to produce high-end programmes.

But British broadcasters who previously had first refusal on projects from British writers are watching as the people they helped develop are tempted away by bigger budgets and the promise of global reach, dismissing the offer of a slot on a mainstream television channel facing declining audiences.

Earlier this week former BBC director general Mark Thompson warned that the UK was at risk of becoming a “Cultural Airstrip One”, with its studios and writers hired by global companies who are less likely to take risky punts on developing new talent in the early stages of their career – but are happy to pick off individuals who have been given chances.

Facebook Twitter Pinterest The Crown: its creator, British writer Peter Morgan, is in demand by streaming companies. Photograph: Sophie Mutevelian/Netflix

Although he acknowledged that it was a fantastic – and profitable – time to be a top-grade British writer, he raised concerns that investment in distinctly British shows could reduce as Netflix and Amazon target programmes with global appeal.

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This is prompting British channels to fight back, in the knowledge they can’t compete on budgets. Instead, they are offering writers more creative freedom and promising that their shows will be heavily promoted rather than hidden far down the algorithmically driven home pages of major streaming services.

“In the last year the infatuation of talent with [streaming services], Netflix in particular, has abated a bit because people feel their stuff can disappear without trace,” said one senior commissioner at a UK broadcaster. “Lots of writers are saying their preferred outlet will always be a public service broadcaster, particularly if they want to say something about this country, because there is more chance of their stuff landing.”

Many successful British shows – including Fleabag and Bodyguard – are already made as co-productions with US-owned streaming services, with a UK broadcaster sharing the production costs and getting the first rights to show a programme. Netflix or Amazon Video then have the right to show the programme in the rest of the world.

Facebook Twitter Pinterest Peaky Blinders: its distribution on streaming services made it a global hit, says its creator, Steven Knight. Photograph: Robert Viglasky/BBC/Caryn Mandabach Productions Ltd 2019

But there are signs that new entrants to the streaming market are less tolerant of such arrangements. Steven Knight, the creator of the BBC’s Peaky Blinders and the big-budget series See on Apple’s forthcoming TV streaming service, said earlier this week that services are increasingly demanding global exclusivity: “Apple and Netflix are different. Netflix are very happy to work with people. In terms of how people see the BBC, the individuals within those companies know what the BBC represents and know that it’s a benchmark for quality. In terms of the business model – does the BBC take part in it or not? – that’s a decision that they take depending on how they run their business.”

He said he was loyal to the BBC but it was the distribution of Peaky Blinders on streaming services that had helped make it a global hit: “Because of Netflix you’re available in 138 countries.”

The photo of Waller-Bridge enjoying her Emmys success tells a story in itself. It was taken by Josh Cole, the head of comedy at BBC Studios. He previously helped Waller-Bridge make the 2016 Channel 4 series, Crashing – her first big television commission as a writer, which represented a bold investment by a British public service broadcaster in a new talent. The question facing the British TV industry is whether the next Waller-Bridge would go straight from fringe theatre to Amazon.