Interestingly, there's been no mention of Brexit at all in the actual Andy Capp strip. The closest thing I can find to one is this one from July 2, in which Flo laments the closing of the docks. That could conceivably be read as a commentary on the decline of British exports to the EU over the last several years. That's kind of a stretch, though, if you asked me. There've been a couple strips where a politician tries to win Andy's vote, as well, but the politics presented in those are even more vague.
Now, clearly, as a newspaper comic, you don't want to alienate a lot of readers. Since the Brexit vote was early on tagged at running around 50/50 for leave versus stay, any stance that showed up in Andy Capp would inevitably piss off half the readership. So I understand why it wasn't brought up there. That's less of a concern in La Cucaracha because 1) Americans aren't as invested in either side of the campaign, and 2) the strip was clearly written after the vote so there's some level of resignation on the reality of what actually happened.
So then there's the question: would Andy Capp indeed be the type who voted "Leave"? I'll start by saying that Andy's residence is in Hartlepool, and that region was in the 60-70% range in favor of "Leave." The strip debuted in 1957, and demographics show that people aged 55-64 were 81% in favor of "Leave." The "Leave" side was also favored by those with lower education and income; I can't find record of Andy's highest level of education, but it almost certainly did not include college, and the household is always shown to be dirt-poor with Andy perpetually out of work.
So statistically, yes, Andy probably would've voted "Leave."
However, contrary to the suggestion in the comic, Andy was not actually shown to be drunk when the Brexit vote occurred. The June 23 Andy Capp did show him in a bar, but he was in a fist fight. So maybe a concussion is more indicative of why he voted "Leave" than drunkenness.