Financial markets have risen after European Union leaders threw a lifeline to the eurozone's tottering banks.
David Cameron welcomed the deal hammered out by the leaders of the 17-nation single currency bloc in the early hours of Friday, saying they had taken "some important steps".
The FTSE 100 Index rose 78 points on the news - a 1.4% increase - following the agreement in Brussels that struggling banks could have access to the EU's bailout funds without adding to government debt.
The surprise deal came after Italian prime minister Mario Monti and Spain's Mariano Rajoy faced down Germany's chancellor Angela Merkel in a tense summit showdown.
Merkel had come to the summit determined to maintain her hardline position, insisting that there were no short-term fixes on the table.
But she was forced to relent after Monti and Rajoy - with the backing of French president Francois Hollande - made clear they would block any further progress at the summit if they did not receive assistance to curb their soaring borrowing rates.
In response, the yield on 10-year bonds in Italy and Spain fell to 4.5% and 5.8% respectively, away from the unsustainable 7% mark which pushed Greece, Portugal and Ireland into taking a bailout.
The agreement finally came after Cameron and the other nine non-eurozone leaders left the summit at around 1am, leaving the single currency bloc to thrash out their differences.
Arriving for Friday's final session, the prime minister said: "For a long time we have been saying that more action needs to be taken for short-term financial stability - more to recapitalise banks, to use firewalls to drive down bond spreads and interest rates to create greater stability.
"I think they took some important steps forward last night and I very much applaud that. There is still important work to do and that is what we will be doing today."
The "breakthrough" was announced by European Council president Herman van Rompuy.
"We are opening the possibilities for countries that are well-behaving to make use of financial stability instruments ... in order to reassure markets and get again some stability around some of the sovereign bonds of our member states," van Rompuy said.
He said they had also agreed the establishment of a joint banking supervisory body for the eurozone.
The summit had expected to focus on a 10-year road map for reform of the eurozone, setting out proposals for a banking union, fiscal union - and leading ultimately to political union.
A report fleshing out the details of the plan will now be delivered to the next EU summit in October.
Van Rompuy said it would be "a specific and time-bound roadmap for the achievement of a genuine economic and monetary union".
"The aim is to make the euro an irreversible project," he said.