* Deadlock broken on final leg of banking union
* New agency to be set up to shut banks with back-up fund
* No common euro zone backstop foreseen for now
(Adds detail, comment)
BRUSSELS, March 20 (Reuters) - European policymakers agreed on Thursday to complete a banking union with an agency to shut failing euro zone banks but there will be no euro zone backstop for the new fund to help cover the costs of such closures.
All-night talks ended a stand-off between the European Parliament and euro zone countries over the new scheme, completing the second leg of banking union that is due to start this year when the European Central Bank takes over as watchdog.
The banking union, and the clean-up of banks' books that will accompany it, is intended to restore banks' confidence in one another and boost lending across the currency bloc, helping foster growth in the 18 economies that use the euro.
It is also supposed to break the vicious circle of indebted states and the banks that buy their debt, treated in law as 'risk-free' despite Greece's default in all but name.
The details of the compromise, which must still get rubber stamped by the whole European Parliament and European Union finance ministers, are outlined in a draft agreement and were confirmed by people involved in the talks.
Under the deal reached, a 55-billion-euro fund made up by levies on banks will be built up over eight years, rather than 10 as originally envisaged. Forty percent of the fund will be shared among countries from the start and 70 percent after 3 years.
It also envisages giving the European Central Bank the primary role in triggering the closure of a bank, limiting the scope for country ministers to challenge such a move.
The fund however, will not be able to rely on the euro zone bailout fund to borrow extra money if it runs out of funds. Critics say this meant that the banking union will never live up to its name.
"The key to the banking union is an authority with financial clout. They don't have it so we don't have a banking union," said Paul De Grauwe of the London School of Economics.
"The whole idea was to cut the deadly embrace between bank and sovereign. But if a banking crisis were to erupt again, it would be back to how it was in 2008 with every country on its own."
(Reporting By Tom Koerkemeier and John O'Donnell; editing by Adrian Croft)