The Greek finance ministry has submitted legislation, required by a deal struck with its international lenders, to parliament.
Prime Minister Alexis Tsipras has until Wednesday night to pass the measures, which include VAT and pension reforms, in order to start negotiations with European creditors on a third bailout.
Greek Prime Minister Alexis Tsipras faces a showdown with rebels in his own party and coalition partners as he battles to win support for the third bailout offered by the eurozone leaders.
The terms imposed by international lenders led by Germany in all-night talks at an emergency summit obliged Tsipras to abandon promises of ending austerity.
Instead he must pass legislation to cut pensions, increase VAT, clamp down on collective bargaining agreements and put much of the country's economy in the hands of its creditors.
If the deal falls through, Greece's banks face collapse and the country could finally be forced to leave the euro.
The latest bailout is conditional on Greece passing all the agreed reforms - including raising tax revenue and liberalising the labour market - in parliament by Wednesday.
Finance ministers from all 28 EU countries are holding a scheduled meeting in Brussels later this morning, where they will discuss the situation in Greece.
The Chancellor is seeking to block any move by the EU to use hundreds of millions of pounds of UK taxpayer's money in the latest efforts to rescue the Greek economy from oblivion.
In a series of telephone conversations with counterparts ahead of a meeting in Brussels later today, George Osborne is said to have made clear that ignoring a 2010 agreement by using the EU budget as collateral against short-term loans for Athens was a "non-starter".
A Treasury source said: "Our eurozone colleagues have received the message loud and clear that it would not be acceptable for this issue of British support for eurozone bailouts to be revisited.
"The idea that British taxpayers' money is going to be on the line in this latest Greek deal is a non-starter."
Banks in Greece will remain closed until Thursday, the country's finance ministry has confirmed.
Greece's banks have been shut since 28 June.
International Monetary Fund (IMF) Managing Director Christine Lagarde said that the deal on Greek debt is "a first step."
Without doubt, we have the feeling that it's a first step to rebuild growth. Now we have to implement the measures and continue with the steps.
Many Greeks have reacted angrily to news of the deal agreed by eurozone leaders, with many directing their anger at the German Chancellor Angela Merkel and especially towards finance minister Wolfgang Schaeuble.
Newspapers laced the morning's headlines with references to World War Two and railed against what they see as Berlin's attempts to humiliate Greece.
In particular, Greeks bristled at Schaeuble's proposal, which was not included in the final deal, for a temporary Greek exit from the euro zone, which many saw as tantamount to expulsion by stealth.
A poster depicting a defaced image of Schaeuble on the wall of a Eurobank branch in Athens highlighted the anger felt by some on the streets of Greece.
Greece is to extend the bank holiday for two more days and will reconsider the situation on Wednesday, Reuters has been told.
David Cameron has welcomed the Greek debt deal, saying it gives stability in the eurozone a chance.
The Prime Minister said: "What's in Britain's interest is that there is stability in the eurozone and there isn't the threats of uncertainty and instability and I think this deal gives that sort of stability a chance. But obviously there is a long way to go to put into place all the things that have been agreed."
George Osborne has cautiously welcomed the Greek deal, but said: "we need to make sure it works for our country as well as the rest of Europe."
The Chancellor added: "What we really want to see is this turned into a lasting solution. Because this risk from Greece hangs over the whole European economy, including Britain."