As a scientist working in a government research facility, the whole concept of the UK leaving the EU has a number of direct effects on me, the most obvious is that science has always worked better when people with the best scientific record are allowed to work together and not just because somebody has a PhD and comes from the UK. At the moment research councils (as well as universities) have worked to this and the freedom to work across the EU has been vastly beneficial to this process. In the future when I'm looking to hire a new researcher into the group any applicant from outside of the UK may have to go through the same considerations as anybody from the rest of the world, what that effectively does is make a larger portion of the CVs being considered less of a sure thing. It'll be interesting to see if the current UK native research applicant number goes up as at the moment very few go into pure research after doing a PhD, they tend to go to industry instead as it pays FAR better, while non-UK native students are the ones who go down the thankless academic route as it tends to hold more personal credence for them.
We already have real problems attracting the brightest and best to the UK when compared to Germany or the USA, this is only going to make it even harder as many may consider not even applying due to the extra barriers in place.
Of course the funding point has been mentioned already, but let me put it this way, EU projects that the UK may have previously been able to get involved in and been leaders in are likely to become a no go. This may not be true of other European collaborations outside of the EU (i.e. the space program) but honestly, nobody can tell, so much of this kind of thing relies on good personal relationships as well as official ones...
Ultimately what I expect to happen is there will be a huge deficit in funding opportunities for UK science both at the SME level (i.e. small-ish businesses that relies on or contribute to UK research) and at the more obvious university and research council level. UK government will probably fill a bit of this hole, but ultimately the money is already massively stretched and frankly even if they ploughed the £350m in that Boris promised to the NHS, it wouldn't fill the gap. So researchers will look elsewhere for funding, they will be ineligible for EU funding of course and I suspect last on the list for funding within Europe not associated with the EU as other countries will simply be easier to work with logistically.
The most likely place for external funding at the moment is China, the USA isn't really open to funding outside of its borders other than industrial collaborations, so really investment into pure academic research has to come from China and to a smaller extent other rich nations (i.e. see proposed take over of ARM). I expect India to begin to make a bigger impact as there are huge cachets of wealth in Indian industry and of course at the higher levels of government.
To put it into easy terms, I expect:
*Faces around my offices to slowly start to change, the number of UK nationals will remain approx the same or reduce slightly due to less PhD opportunities leading to less researchers
* The number of faces from neighbouring countries to reduce (i.e. Italy/France etc.) as these researchers tend to do a PhD in a UK university and then carry on as a UK based researcher afterwards, these opportunities will decrease plus the ease of doing it will decrease as well, leading to a decreased number.
* The number of faces from China to increase (it is already fairly high across the UK research councils so places not taken by EU nationals will become more open to Chinese nationals)
* More UK research to be funded by Chinese industry (already had two state visits in the past two weeks simply scoping out our capability)
* Less UK research to be funded by EU based industry, except in cases where the industry maintains a UK based presence. A good example would be EDF energy who currently fund huge swathes of UK research, if they start to slowly decrease their UK base then one can only assume funding will follow.
* Smaller universities to start to shrink and close as they really do rely on oversees student fees to survive, less oversees students means they will only target the "best" universities.
If I'm being honest I literally can't see a benefit to withdrawing from the EU for UK science. I'm sure there may be benefits elsewhere but as a UK scientist (and unfortunately it is quite a thankless career so those that do it tend to do it for the love of it) all I can see is reduced funding opportunities and an increased need to become reliant on foreign investment with far more strings attached than EU funding ever had.
From a science point of view EU membership has always been a bargain for the UK economy, it's a real shame we weren't able to put this case across to the public during the referendum period, but government law means UK research councils have to remain silent for a month before and after any democratic process, so all we could do was literally sit back and cringe