I can't share the exact quote with you, but my girlfriend is a Dr in a London hospital department. Her lab basically tells you if you have cancer if you are one of the millions of people who live in or around London.
In her department, which requires high-end medically-skilled professionals, her boss posted after Brexit. The basic gist was "Don't worry, everyone, your cancer diagnosis will still be safe in the hands of our department consisting almost entirely of Spanish, Italian, German, French, Polish, Greek, ...... personnel for the time being".
Throughout the NHS the picture is the same. Majority EU and then Non-UK workers. Or universities. Almost all the major universities have majority non-UK lecturers and professors (which actually means something here - a professor is a much higher grade of personnel than in the US, you'll be incredibly lucky to meet a professor outside of academia).
And it's not just as simple as "things will carry on". My girlfriend came over as an EU citizen. She has "leave to remain", so she can stay and live and work in the UK. But to get permanent citizenship, she would have to marry or go through a lengthy immigration process (including a stupid test asking questions about kings and queens that I, as a natural Brit, would be baffled by). Coming out of the EU could revoke that leave to remain. Nobody's sure at the moment and we only have two years to work that out.
If that's taken away, or the paperwork involved in heinous, or even if the process that's required is overwhelmed by all the EU people working in the UK suddenly applying to stay here, then you have quite a situation that is an awful lot of effort to sit through. And they are already disgusted and feeling unwanted because of the Brexit vote.
It's like a state voting itself out of the USA. Imagine how you'd feel as the out-of-state worker who's just been voted against, made to feel unwelcome, contemplating being in a "foreign" state, and may have to jump through all kinds of hoops to carry on your normal life that you've had for YEARS.
We're going to lose an awful lot of talent, from students coming to our universities to the lecturers teaching them, from the waitresses on minimum wages to the doctors earning a fortune. And there's no way that it will become a zero-paperwork process for any of the above, which just adds costs and hassle.
We're now basically a foreign country. If you're American you may not understand that - do you have automatic right to live in any other country in the world? Because before the vote, we have had that guaranteed for decades. We can just up sticks, go to Sweden and start up a life like anyone else, without even bothering with paperwork or visas.
We've (potentially) just thrown that in the bin, which means a lot of people who found that convenient and wanted to live in Britain are now unwelcome and may be forced to leave, or put under such scrutiny that they decide to go to one of the other dozens of countries just 30 miles away, where they don't have any of that hassle.
Watch the NHS, education, and the large businesses. They're all about to suffer, even if they don't immediately collapse.