I'm inclined to think that Brexit will predominantly have bad effects, on both sides of the English Channel and on both sides of the Atlantic Ocean. But it all depends on what people do next. Although it's a strategic trade-off, I think the EU folks would be far wiser to play this in a "nice" way than a "mean" way. I don't think their overall position is strong enough for "mean" to pay off.
Interesting tax policy, among other, implications for the UK. (Or should I say, the English? - suppose Scotland, Northern Ireland, and even Wales were to leave and rejoin the EU.)
Some years ago, the European Court of Justice (ECJ) seemed to be actively obstructing UK efforts to have strong CFC rules that would protect the UK tax base against sheltering activity that took advantage of EU tax havens. This may have been one reason that the UK switched strategies and decided to set up business as itself somewhat of a tax haven.
Without the ECJ, the UK may be free, if it likes, to go back to the previous strategy. But the thing is, I suspect they've made their choice and are unlikely to revisit it. (This reflects that there are competing strategic arguments for both types of approaches.) I note that the UK apparently was opposed to stronger CFC rules within the OECD-BEPS process, a stance that was not ECJ-constrained.
Of course, with Cameron resigning, we don't know for sure who will be controlling UK tax and other policy in either the short or long term.
Leaving the EU would also presumably free the UK to engage in "state aid" of the sort that the EU has been barring when it comes from the likes of Ireland or Luxembourg. So they could now double down on the tax haven strategy if they like.
I suspect that it is actually, or at least technically, possible for Brexit to end up not mattering all that much. If the two sides sufficiently agree to cooperate, e.g., as a condition of mutually favorable trade arrangements, life could go on with surprisingly little change. But the political dynamics may be wrong for that to happen.
One final small tax policy point: Michael Graetz and Al Warren have argued in the U.S.tax policy debate that the ECJ caused the UK to abandon corporate integration via imputation. Another view holds that the UK was trending in that direction anyway. We now have a test case for the Graetz-Warren claim, unless they can establish a credible "path dependence" explanation for why the UK wouldn't revive imputation, similar to my point above regarding CFC rules et al. (Except, my point relies on the existence of imponderable tradeoffs, whereas they may be more inclined to see imputation as a huge and clearcut policy improvement.)