Speaking before an EU summit in Brussels, Prime Minister David Cameron said:
"The eurozone needs a banking union, but Britain won't be part of it this union, and we've properly protected our interests in the single market."
"The countries in the Euro need to integrate more, need to integrate their institutions more," he added.
"But this change taking place does give us the opportunity to argue for the things that we want to do and get a better deal for Britain," he said.
On the eve of the summit European Commission president Jose Manuel Barroso made it clear that he felt more integration should not stop at the eurozone.
He told MEPs in Strasbourg that agreement on the single supervisory mechanism was crucially important at the summit - the "single most important step for the further deepening and completion of economic and monetary union".
He said it was essential that the summit clearly signalled action via the road map to "guarantee the irreversibility and the sustainability of economic and monetary union and the euro."
Last night EU finance ministers moved closer to agreeing the elements of a eurozone banking union with a single, central supervising body, paving the way for the summit to agree the timetable for introducing the "single supervisory mechanism".
The report prepared for EU leaders also looks at even greater eurozone fiscal integration, with co-ordination of national budget decisions and economic policies, probably after 2014.
Draft summit conclusions also emphasise the need to help the search for jobs and growth by reinforcing the European single market - the one key EU element David Cameron insists must be preserved in any new settlement negotiated between the UK and the rest of the EU.
David Cameron will join another EU summit push towards closer economic integration at the latest gathering of EU leaders in Brussels.
The EU is taking more steps towards what is now officially being described as "genuine" economic and monetary union (EMU).
As a non-eurozone member the UK is not directly involved, but Downing Street fears the necessary tighter economic integration and Brussels-based strict supervision and monitoring of banks could undermine the "integrity" of the EU single market - an EU flagship policy which the UK champions.
David Cameron has described the deal reached at the EU summit as close to the "big bazooka" he wanted to tackle the eurozone crisis.
The Prime Minister highlighted the buying of bonds for countries where interest rates were too high, the seniority of debt, and directly recapitalising banks.
There were one or two important things that took place last night in terms of eurozone action, the sorts of things we have been calling for when we talk about bazookas.
For the first time in some time we have actually seen steps taken that I think the markets will see are trying to get ahead of the game.
They need to be followed through, and I hope there won't be a lot of quibbling and worrying about 'is it too far' and the rest of it.
If they want to save their currency they have got to get on and do it and I think last night's action will help to make that happen.
David Cameron has insisted that Britain should retain control for regulating its banks, and not hand over control to the EU.
David Cameron has made it clear that Britain wants to maintain control over its banks.
The Prime Minister insisted that he wanted the Bank of England to remain in charge of regulating Britain's financial sector.
He also said that British taxpayers should not be asked to bail out eurozone banks.
Shadow chancellor Ed Balls has dismissed a deal on euro debt as "not a big step forward".
He insisted that the policies pursued by David Cameron and German Chancellor Angela Merkel were the wrong ones to sort out the financial crisis.
Yet again, the governments have muddled through and we have not had a decisive step forward. We have not seen the change we actually wanted to see.
I'm afraid we are going to get back to the wrangling and we still have the Cameron/Merkel view which is that big spending cuts will get growth when that is clearly not working.