Curt, and there is also the startups that will be affected.
The current movement of talent within the EU --including the UK-- is beneficial for both well established companies and startups. Many of the founders of European startups have met at university, either in the UK, or another EU country. They work remotedly at the beginning from their different cities.
Many set their headquarters in London and take advantage of Campus London, where they grow with the evening of entrepreneurship, they learn about tax incentives and financial insights, share experiences, and even share office work spaces. This is a Google initiative, and Campus London also provides mentoring sessions with expert Google mentors covering diverse topics.
All statups benefit from this, and they grow as truly global and diverse tech companies.
What will happen after Brexit? Startups will have it more difficult. For UK startups it will be less easy to recruit talent from the EU, and vice-versa. For startups, participating in competitions, attracting VC, attending startup conferences will not be the same. Fees and regulations, which don't exist at the moment might start to block incentives, development, and have a negative effect in the rich startup environment that has been created during so many years now.
London ranks number one at the moment for European startup hubs. In the same way financial institutions, and big enetrprises are talking of moving to the EU, the same is likely to happen with the startups, with the consequences that it implies.
PS. I like what you did with the headline. :)