What are the upsides for British science from Brexit?
There are no upsides for British science from Brexit.
This is a corollary of the almost certain fact that there are no upsides for British society from Brexit.
Science funding has never been a priority of the current government and I hardly expect that situation to change once we leave with no deal. In truth, we are cutting off access to collaborations (e.g. ESA) that we can never hope to compete with as a single, tiny nation with a floundering economy.
To understand, then, why in spite of this 12% of UK researchers still voted to Leave, you have to realise that when the referendum was held, a large number of people in the country used their vote as a protest-- against the establishment, against immigration and against the perceived power of the EU parliament over our own.
People were generally misled by self-serving politicians that societal benefits would occur once we left the EU-- more control over our laws for instance, forgetting that we elect MEPs to the European parliament so have just as much say in EU law as our own. They perhaps believed that there would be more money for the NHS, even though the reason the NHS is underfunded is not due to the EU but due to the same Conservative government that has been in power for the last eight years.
I am certain that not even the politicians gunning for Leave actually thought the benefits they claimed would ever happen-- they simply picked the side they thought would gain them votes, and for many Conservative MPs with very right wing, anti-immigration constituencies this was Leave.
For the reasons I have outlined above (and doubtless many more), a person may have decided to vote to leave. The vote was a very personal decision for a lot of people and as Thomas says, scientists are people too. The 12% that you quote likely voted to leave based on non--scientific issues, just as I voted to remain based on non--scientific issues, namely that I believe that a diverse and multicultural society is better and more productive for everyone, I am averse to hatred and xenophobia and I like going on holiday to other EU countries without needing a visa.
If our politicians were capable of thinking about something other than their own ratings in the polls, they might have been able to negotiate a sensible leaving deal, with every eventuality considered and taken care of. In that case, I would be less worried about the effects of leaving on British science.
However, we are now faced with the prospect of a no-deal Brexit. The government is trying to hide the fact that it is stockpiling food and mobilising the army to prepare for the worst (presumably they are afraid of rioting and looting).
People's wilful ignorance of the wholly negative effects of Brexit will be sorely tested when food rots in the fields with no EU workers to harvest it, when a black market begins for "luxuries" like cheese and chocolate, and when their relatives die in hospital because their medicine is on the other side of the border.
Society will suffer. Science will suffer.
I am aware that this is an emotive and partisan answer, but Brexit is a very emotional subject for most British people. I am still living in hope that one day soon we will have a general election, form a sensible government and call the whole thing off.
Scientists are people too. They may vote for Brexit for non-academic reasons. For a list of (non-academic) reasons in favour of Brexit, see http://www.voteleavetakecontrol.org/why_vote_leave.html
Many academics may think that Brexit will have minimal impact on academia. The UK government has given assurances that it will make up for any lost EU research funding. And EU research funding is available to some non-EU countries. So perhaps they are won over by non-academic arguments about immigration, costs, trade, and regulation.
Of course, every individual has their own reasons for voting one way or another. Some may just view Brexit as an anti-establishment protest vote. I can only speculate!
How someone votes is not purely based on their job, so trying to makexplain useful inferences about how an academic scientist thinks Brexit will affect science based on voting patterns is probably a worthless endeavor. Had the politicians promised massive increases in science funding as part of Brexit, it is not clear to me how many academic scientists would have changed their votes. The vast majority of academics object to Brexit for a number of reasons not directly related to their jobs.
As for the effect on academic science, the one major benefit will likely be an increase in the number of full fee paying international students as EU students will presumably not get discounted fees.