The science thing is something I'm particularly interested in with my work, and it's a basic fact now that not only is the vast majority of research collaborative, but a significant chunk of those collaborations are international. Now you could justly argue that this will continue, that academics at British universities are among the best in the world and will continue to operate with peers around the world. That is undoubtedly true, but what programs like Horizon2020 do is make those collaborations easier. Being outside that will add a hurdle that needn't have been there. May has suggested we might continue paying into certain programs, and you'd imagine H2020 (or H2027) will be one of those, but it's all very uncertain, so goodness only knows what researchers looking for partners and/or funding are doing at the moment. And that's before you get onto things like data sharing and the movement of academics.
When I posted up something on the topic a few days ago, Joe brushed it aside as irrelevant. I'm off to take some deep breaths.