It's affecting a lot of us at my work - a university. I don't currently have any EU grants but worked on EU funded projects for many years and hoped to do again - but now we can't join the applications. Yes it's possible that post-Brexit there will be a way for British academics to participate on EU projects but we won't know for several years. Also, I work in social science/social policy and that has tended to be much better funded by the EU than by the UK government and research councils, so even if money is diverted by the government to British science it's unlikely to fund my field.
So that's having a big impact.
Plus long term colleagues from EU countries are looking for jobs elsewhere, even though they could probably get residency that is tricky for some of them in various ways. And everyone wants to be able to participate in EU grants and networks so the temptation to move to EU countries is strong.
I had been planning to move to Spain or France in a few years, and work there, but this plan is now much more complicated. Again, it may be possible but it's impossible to plan without knowing the terms of Brexit and how it will affect movement and jobs.
Plus we run postgrad courses with many international students and I think now the EU ones are likely to pull out as they can't be sure about funding and visas. But we won't know the details of that til September.
So I'm in a depressed limbo, but on the plus side (here is a positive for Bertrand Russell), everyone at work in my university is pretty depressed and anxious so there is a solidarity to the sense of horror/anxiety/uncertainty. I've never actually seen the university sector united on anything before - from vice-chancellors to staff to unions - this is unusual.
DP's company has stopped hiring due to Brexit, so he's worrying about future work possibilities (lots of redundancy and contract work in his sector - IT).
DD was thinking of applying to university in the Netherlands, she'd been working towards this and this is now on hold.
So a lot of change and uncertainty, and some of it is anxiety about things that MAY be OK in the long run but it is so very hard to plan and you need to plan a few years ahead for grants/student numbers/moving abroad/university places.