* Commission may propose supervision rules in Autumn
* EU leaders explore deeper integration
* Britain will not join any banking union
By John O'Donnell and Luke Baker
BRUSSELS, June 13 The EU executive could make proposals this autumn to integrate supervision of banks, the head of the bloc's executive said on Wednesday, outlining a key step towards a banking union to underpin the euro zone's financial system.
Jose Manuel Barroso, President of the European Commission, said that it could present legislative proposals to integrate European supervision.
Officials expect this to include strengthening the European Banking Authority, the EU's fledgling supervisor.
"By Autumn the Commission could be ready to come with key proposals to introduce more integrated banking supervision and common deposit guarantee and resolution funds," Barroso told lawmakers in the European Parliament.
EU leaders will discuss establishing closer ties at a summit scheduled for June 28-29, and a draft statement prepared for them to deliver after they meet underscored the need for banking and fiscal integration.
"There is a need for more specific building blocks centred around a much stronger banking and fiscal integration, underpinned by enhanced euro governance," said the text, obtained by Reuters. "Recent developments have demonstrated the need to take the EMU (Economic and Monetary Union) to a further stage."
However, steps towards such integration are politically difficult. They could include the creation of a so-called banking union to centralise control of big European banks and EU funds to wind down problem lenders or reimburse depositors.
Britain is opposed to signing up to such schemes for fear of losing autonomy over the City of London, Europe's biggest financial centre. Earlier this week, Britain's financial services minister Mark Hoban said it would not join any such union.
"People in Brussels understand that we won't be part of it but that we support a banking union for the euro zone," said one British diplomat.
Barroso signalled that even were some countries to reject such schemes, others should press ahead. As well as a likely British opt-out from a banking scheme, opposition from states including Germany have so far hindered the creation of single EU fund to protect depositors or cover the costs of closing banks.
"We must recognise that some countries do have opt-outs. These opt-outs must be taken into appropriate account in the future architecture," Barroso said.
"Those who wish to advance must be able to do so," he said. "But enhanced cooperation or properly circumscribed derogations can allow for this without creating a risk for the integrity of the European Union."
Barroso, alongside European Central Bank President Mario Draghi, Eurogroup Chairman Jean-Claude Juncker and European Council President Herman Van Rompuy have been given the task of reporting to the summit on closer euro zone integration.
"The report commissioned ... on steps towards a full economic and monetary union will set out the main blocks, some concerning all the member states of the Union, others only the members of the euro area and, as appropriate, others willing to join," said the draft conclusions prepared for the 27 leaders.
Moving towards a single chief EU supervisor may take time, said Nicolas Veron, an expert in financial policy with Brussels think tank Bruegel.
"It took more than a century to move from purely state banks to a national banking system in the U.S.," said Veron. "You won't be able to centralise everything over night in Europe."