Could you really not have managed to fit that on one post?
Anyway, I meant domestically but as you ask about internationally... The EU wants to be seen as one body, which means removing our own international representation. We have 1/28th of a say in the EU (which is often at odds with the rest of the EU, comparatively with other members) which is compared to the whole say of the UK which is the 5th largest economy, an important member of NATO and on the UN Security Council. The UK has a lot of say on its own, in the EU, not so much.
Really, you want to reduce it to 1/190th of a voice, without a guarantee of so much as being heard, and no plan of action? Went to any world summits lately? Climate change panels? Chatted with Monsieur Putin on the phone lately? And that's just kid's play to start with. We went into the bloc for a reason; relying on the NATO/UNSC stick isn't as good a 'gunboat-lite' approach as you think, especially if you can't or won't face direct conflict on a massive scale for minor gains. It has its uses but won't replace the other geopolitical and economic advantages the EU brings. Even the generals in charge think so, and are baffled by us wanting to scupper NATO+EU cooperation on the matter. I mean, you do realise that both your NATO and security chair is predicate on your ability to keep up with security contributions, regardless of what your economy is going through. Without economic clout, there's no global influence, and both for us are greater in the EU.
Hopefully the recent Cameron venture amply demonstrates -- international agreements aren't as easy as going it alone, and hoping for the best outcome. Now imagine the same attempted within an even looser framework of negotiations against national economies in the ballpark figure of the EU as whole, say the USA and China, how well do you think we will come out of it all without the bloc's clout and a list of fanciful demands? How would you effectively prevent dumping strategies, for example, that even neoliberal economists would warn to take action against, when you're 1/10th of the economy of your foreign counterpart?
Besides, the key Commonwealth figures are warning that increased trade on their part won't compensate for EU losses we would incur by departing (though small shop owners and media personalities disagree); so you'd already be starting you re-negotiations with Europe post Brexit and the world with a massive handicap and a real sense of desperation. Nothing 'great again' can emerge from that.
Say what you will, whatever your political ideals are, a sound economic plan is needed to pay for the whole shebang, in or out. The ins have economic cred, the outs not even a hot mess on paper, and are pressing ahead against the majority of independent economic advice.