David Cameron is attending another EU summit push towards closer economic integration after an overnight deal to set up a new system of tougher banking supervision for the eurozone.

An early-hours accord between EU finance ministers meeting in Brussels paved the way for the summit later on Thursday to endorse a single eurozone banking supervisor - the backbone of a full banking union to reassure markets and to protect the single currency from future financial crises.

The move takes banking oversight out of the hands of national eurozone authorities for the biggest EU banks - a plan backed by Chancellor George Osborne after he won safeguards against interference in British banks.

Mr Osborne warned fellow finance ministers against giving the European Central Bank - the new supervisory authority - any powers over eurozone banks in non-eurozone countries when the UK national bank regulator would have no such powers in reverse.

For example, he said, it would be unfair and unacceptable if the ECB had supervision powers over Deutsche Bank in London when the Bank of England could not exercise similar powers for HSBC in Paris. But some other non-eurozone member states may choose to submit their banks to the new ECB oversight - if only to benefit from the expected renewed market confidence in areas of the European banking sector deemed to be under tighter regulation in future.

The Chancellor also won assurances over the UK's voting clout in the work of the London-based European Banking Authority, which stress-tests the resilience of the European financial system, and sets rules for all EU banks, inside and outside the eurozone. It had been feared that the onward march of eurozone controls would marginalise the UK and the other nine non-eurozone member states when it came to setting banking rules for all 27 EU countries.

At the summit, which continues on Friday, EU leaders will be considering a proposed "roadmap" which, alongside eurozone banking supervision, calls for new measures on bank "resolution" - how to handle failing banks - and how to set minimum standards for deposit guarantee schemes.

The 15-page report prepared for EU leaders also looks at even greater eurozone fiscal integration in future, including co-ordination of national budget decisions and economic policies, with potential fall-out for the harmonised single market.

The Prime Minister will warn that the necessary tighter economic integration under consideration for the eurozone must not be allowed to undermine the "integrity" of the single market - an EU flagship policy which the UK champions.

Mr Cameron has already made clear that the single market is the one key EU element which must be preserved in any new "settlement" negotiated between the UK and the rest of the EU.