Apart from its political and constitutional relationship with the eurozone, something else is at stake for the UK at the European Union council: whether we are propelled back into hideous and serious recession.
British jobs - lots of them - are at risk if the eurozone doesn't sort itself out.
And right now, it doesn't look as though eurozone leaders have come up with a sustainable solution to their debt crisis.
The implicit borrowing costs for Italy and Spain - two eurozone governments with very substantial debts - have risen sharply.
In the case of Italy, the yield or de facto interest rate on its five-year debt went through the punitive and unaffordable 7% threshold again early this morning and is now a high 6.9%.
As for Spain, its borrowing costs are lower: the yield is 5.9% for 10-year debt, but that represents a painful 0.7% jump over just two days.
Investors looked at what EU government heads agreed last night and see it as yet another example - the fifth - of measures that might have reassured a few months ago, but are now inadequate for the task at hand.
Which is not to say that there's no progress.
But here's the scale of what's at stake.
Eurozone banks can't borrow in dollars - the world's most important currency - from commercial sources. They are more and more dependent on support from the European Central Bank and on funding themselves on a risky, short-term overnight basis.
A number of eurozone banks are as reliant on official central-bank funding as Northern Rock became in the autumn of 2007.
Put it together and what you see is exactly the conditions that prevailed before Lehman's demise tipped us over the edge in the autumn of 2008.
There is a danger that at some point a big commercial bank will run out of the collateral or assets needed for emergency borrowing from the European Central Bank or its relevant national central bank. And at that point, said bank will go down, risking a domino effect of collapses throughout the financial system.
So in those dire circumstances, one and a half steps forward from eurozone government heads are almost as bad as none at all, when investors want the full two.
The full two steps include a proper, formal integration of decision-making on taxing, spending and borrowing within the eurozone - and not the complex, cumbersome mechanisms that have been agreed for spanking governments which breach a borrowing threshold that was (in any case) rarely breached in the run-up to the debacle.
The necessary steps would also involve full "mutualisation" of eurozone sovereign debt, the pooling of sovereign liabilities, which would permit the European Central Bank to be the lender of last resort to the currency union - and give the eurozone the kind of protection against the risk of default that the UK and the US have.
The problem is that when you see what's required by investors, it is difficult to be optimistic that we'll ever get there.
Well it's doubtful that France, with its strong Gaullist traditions, will ever surrender sufficient control over budget-making to a centralised extra-territorial authority (Brussels or Berlin, depending on where you think the power would in practice reside).
And when we talk about "mutualisation" of eurozone sovereign debt, that's a euphemism for Germany underwriting all eurozone nations' debt - and it seems unlikely that, when put that way, the German people will find that more appealing than a plate of cold sick.
So after this latest EU council, we will have several days of arguing about the technicalities of what's been agreed.
Optimists will point out that 500bn euros of bailout money should be available for use reasonably quickly to prop up the likes of Italy and Spain, as a result of the leaders' decisions to expedite expansion of the European Financial Stability Facility and bring forward the launch date of the European Stability Mechanism.
Pessimists will note that 500bn euros is about enough to keep Italy afloat for 14 months.
As for the UK, well - depending on whether you are a European Union fan or foe - you will either agonise that the prime minister has removed us to the EU's remote periphery where our ability to influence decisions affecting our vital commercial interests will be minimal, or you will moan that the prime minister has failed to repatriate vital powers back to Parliament and people.
And there will be hand-wringing about whether UK taxpayers should be increasing their potential financial exposure to the eurozone's debts by participating in a 200bn-euro top-up of the International Monetary Fund's resources.
All of which may feel like life-and-death issues that go to the heart of our constitution and national identity. But if that great ship called the eurozone does hit the iceberg, and there is a calamitous collapse in markets and economy, nothing else would feel terribly important at that fateful moment.
Update, 1545: The Treasury is more than a bit miffed by the French accusation that it was trying to protect the narrow, short-term commercial interests of the City by watering down financial regulation as part of the protocol that the prime minister wanted in exchange for allowing an EU treaty change.
In fact, one important demand made by David Cameron was that the UK should have the ability to impose tougher regulations than the standards contained in forthcoming directives.
In that sense, the big banks should probably be cheering for the French rather than for HM Treasury or the PM.
As I've noted here before, the Treasury has been concerned that the new Financial Policy Committee at the Bank of England would be prevented by EU legislation from forcing banks to retain more capital relative to their assets as a dampener on incipient lending booms.
The Treasury is also concerned that some of the Vickers recommendations, which go much further in limiting banks' room for financial manoeuvre than EU rules, could be blocked by EU rules.
So perhaps the City should be grateful to President Sarkozy for rejecting the proposed British deal on financial services - although maybe many of the rest of us should be slightly anxious, if there is scope for the EU to hobble attempts to sanitize the City.