Existence of regional bias in peer review and how to deal with it
Is there concrete evidence out there to suggest that such discrimination at peer-review happens?


Yes, there is. This is the most famous example, having been cited (as of time of writing) 1167 times. The author took 12 already-published papers written by authors from prestigious and productive American institutions, changed the names, added fictitious institutions, and resubmitted them to the same journal. Three of the resubmitted papers were detected. Of the remaining nine, eight were rejected for serious methodological flaws.

There're a lot of possible explanations for this, of course. One could simply be that peer review is random. Another is that methods have improved since the original publication, so the claim of serious methodological flaws is justified. Or perhaps it's just bias. It's for you to interpret.

Here's another article that deals with bias in peer review explicitly. Three of the biases investigated are prestige bias, affiliation bias, and nationality bias. There is some sign of bias, but as is typical in the social sciences, nothing is clear-cut.


  How can we deal with this kind of problems (for example, potentially submitting to journals that follow double blind reviews, etc.)


I don't think there's any good option unfortunately. Double-blind peer review simply isn't very common right now, and it's not easy to submit to one anyway (you will have to modify your paper, anonymizing any self-references). Triple-blind peer review would be even better, but there are even fewer journals that practice that. Unless and until these become more common, you'll probably have to put up with it.