David Cameron has called for swift moves towards a banking union for the eurozone without compromising the EU single currency.

The Prime Minister told fellow EU leaders at a Brussels summit that Britain backed the plan, including sweeping supervision not just for the biggest banks but smaller institutions too.

He later, over dinner, set out the need not just for a single supervisor to govern the eurozone, but for a comprehensive system of resolution funds – to cover the wind-up of failing banks – and deposit guarantees to restore stability and credibility.

None of the measures would affect non-eurozone nations, but Mr Cameron was seeking assurances that further integration would not be at the expense of the single market.

Mr Cameron said: "We're in a global race. We need to make sure that we're competitive, we need to make sure the European Union is competitive. And that means deregulation, cutting the costs of regulation, supporting enterprise, it means doing trade deals with the biggest economies in the world, the United States of America, Japan, the fastest growing countries in the world.

"Above all it means completing the thing that matters most for us in Europe, which is the single market. That could be an engine of growth and there's more work to be done."

British pressure to keep up the pace in the face of the economic crisis came as French President Francois Hollande told Britain not to try to dictate to the eurozone.

Mr Hollande said: "Certain countries don't want to join [the eurozone]: that's their choice. But why should they come telling us how the eurozone should be run?"

Mr Cameron was hinting at British support for a separate budget for the 17 eurozone countries in the longer-term.