Leaders in the UK tech industry have warned that the government’s removal of a visa cap for skilled migrants may not go far enough to ensure Britain continues to attract the best people from across the sector.

On Thursday, Theresa May announced that healthcare professionals would no longer be counted against the capped number of tier 2 visas the government issues to skilled workers, in effect adding another 8,000 or so to the 20,700 applicants allowed into the country every year.

The news was welcomed by the technology sector, which has been experiencing an acute talent shortage in recent years, as an increase in demand for key skills such as data science is impacted by the British immigration system.

But founders and funders alike said the extra visas were not enough to keep the Britain’s tech economy ahead of the rest of Europe.

“Talent is obviously the single biggest concern for any founder and any company being built in the UK right now,” said Ophelia Brown, a founder of London-based venture capital firm Blossom Capital. “To build a world-leading company and world-leading products you need access to the best talent across the globe.

“This announcement is a very welcome first step – but it is just a first step. If we don’t do more on this, we run the risk of losing our edge in the tech sector.”

The newly freed-up tier 2 visas will not just be for tech. The sector will have to fight other areas of the economy to justify its hiring – and May’s announcement was widely seen as a gift to the City, rather than the Silicon Roundabout.

Other government policies are more directly aimed at helping entrepreneurs, however. The secretary of state for digital, culture, media and sport, Matt Hancock, told the Guardian last week: “I’m in constant discussions with the tech industry about how … we can have a visa system that both controls immigration, and ensures that the brightest and the best talent from around the world can come here.”

On Wednesday, Hancock announced another step towards that goal: new startup visas, to be introduced in 2019. An expanded version of the old graduate entrepreneur route to residency, Hancock said the UK would “have a Dragons’ Den style approach so accelerators and entrepreneurs can choose who has the best ideas and then the visa scheme follows.”

But Brown cautioned that even that announcement “affects a smaller number of people than is needed. When you’re building a company, it’s more than just the founder team.”

Hovering in the background of the issue is Brexit, which founders say is scaring away potential recruits who do not even need visas to work in the UK. Tugce Bulut, the founder of the Streetbees business intelligence platform, has lost multiple engineers to emigration since the EU referendum two years ago.

“We had excellent engineers who had relocated to join our company,” she said. “When it came about, they were immediately very concerned about what would happen. A lot of tech people prefer a more stable option in their life, they don’t want to take huge risks.”

One coder returned home to the Czech Republic, quitting his job and ultimately gaining employment with a local company. Several others, she said, emigrated back to their home countries but continued working remotely as contractors – keeping the company staffed, but depriving the UK of the tax revenue they would otherwise have contributed.

Even if the UK does expand its visa programme to meet demand, Bulut warns that the government’s “hostile environment” policy will be hard to counter. “There are two other things that are very important: what is the public spirit like? Why would you go to a country where you don’t feel welcome?

“And the second factor is: what are the politicians saying? What is the political discourse? If there’s an active discourse against immigration – this is the best of the best talent we are talking about. They have a lot of options. They would go somewhere that they feel welcome.”