My money is on the central/eastern countries, if they are forced to accept refugees.
The UK leavers have pretty much admitted that migrants are still going to come despite the Brexit vote and the EU has categorically stated that there is no access to their market without accepting the free movement of people.
If any country leaves the EU because they think that's going to solve the refugee problem they are not paying attention very well.
That doesn't make sense. Pulling out of the EU *means* leaving the Single Market. EU nationals will not have a right to live and work in the UK without some kind of visa or agreement in place; UK nationals will likewise not be able to live/work in EU member states. The UK will be able to turn away anyone at the border who does not have a right to enter.
The UK will have to make some kind of agreement with the EU for trade, or fall back on the WTO rules. So there will be *access* but it won't be tarriff free, automatic access.
Solving the refugee crisis requires something completely different; and that is making the originating countries somewhere that people want to stay. Unless you are going to accept each and every person from a country/region, taking in a few (as a percentage) just encourages more. It's ludicrous.
Of course, that's a completely different story (ie, who makes and sells all the weapons? Oh, the US, the UK, France, Germany, Russia...).