I guess that a Brexit would degenerate English football back to the old kick the bladder level of before Schengen. I think that that alone would scare the hell out of anyone in Blighty. Nor does it spell much good for the quality of weed if the Harwich to Hoek ferry has to unload with increased customs attention. Granted, the Brits never experienced the benefit of the Eurozone as much as I did on my many travels out of my minute country, but looking at the quality of the political debates in most EU countries I would state that the EU institutions are an absolute bliss to overcome the xenophobic neuroses that have gotten hold of them.
Now surely there is a lot amiss with the amount of democracy in the institute and as such it is a bit far fetched to have much confidence in federalisation of the EU. But the alternative of going back to medieval city states and Swiss model valley clans doesn't appeal much either. The desire for cultural inbreeding may be strong, especially in the land of Cheddar and Marmite, but surely some of you Brits have enjoyed some of the benefits of the EU.
On accord of the fear for Federalisation I'd say, take a look at the US and China. Both are inhabited by populations that don't care much about foreign policies as long as they're happy enough. They are ruled by incompetence on all levels and still manage to amaze the world. Neither is all that liberal on immigration, but freedom of movement internally has clear benefits, though the Chinese migrants are clearly worse off as migrants are second class citizens to the local City dwellers (no benefits, no school for their kids). Both states have clear cultural differences internally albeit not as strong as in the EU for the most part, but that has more to do with ethnic cleansing in certain periods of their ongoing history. That however is not very likely to happen in the EU any time soon. Last time it was tried it hardly made an impact on diversity of cultures, though some cultures suffered horribly.
And if you Brits feel unimportant in the EU as it is, what do you think will happen once you have become the North Korea of Europe? Trade agreements? Sure... but don expect much of it as there has to be a certain price for leaving the EU to prevent further disintegration, even if it comes at some economic cost. The latter not all that significant in many respects either from the continental side and some states will see the opportunity to increase internal exports that are now in UK statistics. Nor do I expect the UK to survive very long as a British federation. There are quite some voices in it that are less than pleased with their overlords implementing insane rules and having quirky manners.
It's a can of worms that has been opened,.. enjoy.