I don't get where you are coming from GB. The UK and Germany are pretty much carrying the EU. It would make sense for the UK to jettison the ugly sisters like Greece. I'm surprised Germany hasn't pushed to do the same.
Yes there are benefits to the EU. I just don't see it for the UK and Germany. Might be different if it was more of a free trade pact than a single currency. That is what it started out to be. I personally think the weak sisters need to fail like Venezueala. That will change their attitudes real quick about socialism.
Care to explain in a little more detail? I am really interested in your opinion as why this is a complete tragedy. 
It's more a 'Leadership and destiny' thing with Germany than an economic one, though there is an economic aspect too in that as one of the most industrialized and productive countries in Europe, Germany sees open borders and a unified currency as advantageous to it as an exporter. UK is somewhat hampered in the productivity department despite high industrialization, there is a rather stupid tradition of strong unions and low productivity there, much like France but not as bad. Of the other players making 'Leave' noises, Dutch discontent is probably the most economically-based, while in France it's more nationalistic than economic.
Free trade, as implemented in the last eight years and to some extent under the two previous Presidents, has been a whole lot better for the stock market and US banks than it has for the US manufacturing sector and actual workers, both of whom have steadily taken it in the shorts as US exports have been frozen out of overseas markets while our gates have been flung wide, reducing us to mainly an exporter of lumber and mineral resources, plus a few unique tech items, and otherwise a net importer of about everything else. It's been a disaster for our manufacturing sector and skilled manufacturing employment, but it's been great for people whose incomes are dependent on stocks and investment. The stock market's rise is touted as great economic success, however it is really a Potemkin village with rot, decay, and ultimate disaster lurking behind the facade. You can tell a lot about where a poster's money comes from by how they feel about free trade arrangements like TPP.
As far as NATO goes, it has somewhat lost direction since the end of the Cold War, though a resurgent Russia indicates ending it is not really a good idea. At the same time, with no active threat on the border, it drifts without purpose, with the US bearing any burdens for any actual international action that involves someone's army actually leaving its own home territory, to the extent their military forces are anything more than cadre or hobby establishments in the first place. The really basic problem that neither proponents or opponents want to touch is that the EU and NATO are fundamentally contradictory establishments. NATO exists (From our POV) to align smaller European countries behind our interests and construct a sphere of influence where we dominate. The EU on the other hand excludes the US, which has no interest in joining it and would not be welcome even if it did have any, creating an independent sphere which in theory can use its united economic power to deal with either East or West to its own direct advantage without reliance on the US.