I think had Tony Blair had his way that's what Britain would have done, he was a leader that other European leaders seemed to look up to and respect unlike Cameron who gets treated with disdain (especially by Sarkozy when he was there), Blair's vision would have been that he would have been the big fish alongside his adoring fan Gerhard Schroeder and Britain would have been one of the dominating powers in Europe. However the country as a whole was not in step with Blair's Euro-enthusiasm and Blair would have also had us in the Euro which would have made our recent financial problems a lot worse if we hadn't had the independent Bank of England to lessen the pain.
I wish the single currency had never gone ahead as its the single biggest balls up in the history of the EU and it seems the countries inside are not going to cut their losses and end it but trying to go all in and have a giant fiscal union which means they will have to become much closer on tax rates, budget balances and all sorts. The Germans seem to be driving this but if it is to work then they have to accept the inevitable consequences - the United Kingdom is a fiscal union where the rich regions of the UK end up subsidising poorer regions through transfers of revenues and Germany as the richest part of the EU will inevitably have to subsidise the poorer parts. They have to accept this from the start.
What I fear will happen is Germany will lead calls for a fiscal union, so that it can keep on being inside the Euro which means it has a currency much undervalued compared to what the Deutschmark would be on its own, making German goods much cheaper in Euros than they would be in Deutchmarks hence Germany has a huge export advantage. But they will constantly complain about having to subsidise the others, and castigate them for having higher unemployment, lower productivity, and lecture them on how they need to have lower wages and conditions etc. Unless Germany is willing to accept the rough with the smooth of fiscal union it is not going to work.