Northern Rock and the central bank

Following the story over the weekend, and fascinated by the sight of a traditional "run on the bank", I also saw, as expected, the government and the Bank of England team up to guarantee the bank's savings deposits. The Bank offers a line of credit, and the government essentially underwrites as much as is found to be necessary. The government's support is underwritten by the taxpayers.
All perfectly normal, good practice. One thing did occur to me though. I am not sure that such a co-operation to protect a bank could happen in the euro-zone.
As I understand it, the European Central Bank is different in that it is not linked to a government with tax-raising power. Uniquely, it is entirely independent and while it holds the currency reserves of the dozen or so central banks in the zone, the implicit or explicit support of the taxpayers of Europe is not extended to supporting the ECB.
Now, I may be wrong in this. Perhaps the central banks retain the power to issue credit without limit to a bank in trouble. Perhaps the ECB has power to do this anyway. But I am sure that this is what I read years ago when the euro was getting off the ground. It was seen (perhaps by Bernard Connolly) as a fantastic, grotesque gamble with the savings of most Europeans. The politicians were gambling that they could get a constitution in place before a financial crisis (such as had happened with the American S & Ls a few years before) came along and wiped out savings.
Anyone correct me on this?