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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.
Latest ITV News reports
David Cameron has said he will use the summit of EU leaders to push for "a better deal for Britain in Europe".