Prime Minister David Cameron is resuming talks with other European leaders after urging swift moves towards a banking union for the eurozone without compromising the EU single currency.
Overnight a preliminary deal was reached to create a supervisor for 6,000 banks in 17 eurozone countries.
Mr Cameron had told fellow EU leaders at a summit in Brussels on Thursday that Britain backed the plan, including sweeping supervision not just for the biggest banks but smaller institutions too.
And over dinner later he was setting 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 countries, but Mr Cameron was seeking assurances that further eurozone integration would not be at the expense of the single market.
Arriving at the two-day summit the Prime Minister 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. And 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 continuing economic crisis in Europe came as French President Francois Hollande effectively told Britain not to try to dictate to the eurozone.
In an interview published in a group of papers across Europe, 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's case is that measures being taken inside the eurozone must be closely studied to ensure they do not impinge on the rest. He was even hinting at British support for a separate budget for the 17 eurozone countries in future - although the idea is far off and for the moment Mr Cameron says he can not see how it could be introduced without implications for the wider EU budget.
Before the summit Mr Cameron held talks with his anti-federalist European political bedfellows, including the leaders of the Poland's Law and Justice and Poland Comes First parties and the Civic Democratic Party of the Czech Republic. The parties formed a new political bloc in the European Parliament after Mr Cameron took his MEPs out of the mainstream centre-right grouping, the European People's Party, in 2009.
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