Consider applying to Scottish universities. Back in 2014 when Scotland was voting on whether or not to leave the UK, one of the key arguments was EU membership. The "No" campaigners argued that Scotland may not make it into the EU as an independent country, since Spain would be likely to veto their membership to discourage Catalonia from breaking away as well. Whereas in the UK, EU membership would be guaranteed. This uncertainty of Scotland's future ultimately swayed a lot of people towards the "No" vote, as risking EU membership for Scottish Independence seemed like a bad idea.
Now though, England and Wales have voted overwhelmingly in support of Brexit, ultimately dragging the EU-loving Scotland along with them. This "betrayal" by the rest of the UK will undoubtedly be used as an excuse for a 2nd referendum for Scottish Independence. And this time round, not only is independence more likely to gain support, but also the rest of the EU is more likely to want them in. Scottish Independence will hurt the UK, much like the British 'Independence' is hurting the EU. The EU will likely to be supportive of Scotland's bid for independence and membership, as it will discourage other countries from leaving. Spain has already said they would not veto Scottish membership if Brexit happened.
"But why would going to Scottish universities help me?" You may ask. Well, if the 2nd referendum goes by the same rules as the first one, any British national residing in Scotland would be eligible to vote. Thus, as long as you register before the deadline, you would be able to vote "Yes" to Scottish Independence. While independence is likely to be the favourite, it could be very close, so your vote will matter. Also, going to university in Scotland will give you connections to the area, so you may be more likely to find a job there. Thus you'd be more likely to be able to live in the EU after graduation. And a further thing - since Scotland shares a land border with England, Scottish Independence would make it easier for pro-EU UK citizens to move to the EU, so you would help a lot more people than just yourself.
Or does it play no part?