Straw, the former Labour foreign secretary, warned that the euro "is going to collapse," and said, "Is it not better that this happens quickly rather than a slow death?"
Straw's message came after the International Monetary Fund (IMF) said the world economy would be destroyed if IMF members did not aid the Greeks.
Speaking at the parliament, Straw said, "What the Government should do instead of sheltering behind the complacent language, weasel words that 'it is not appropriate, we should not speculate' is recognize that this eurozone cannot last.
"And it is the responsibility of the British Government to be open with the British people now about the alternative prospects."
In an urgent meeting, Britain's senior MPs from all parties asked the government to stand aside from the new financial package aiding Greece and urged the country to leave the euro.
Mark Hoban, financial secretary to the Treasury, said, "I am not going to comment on whether the eurozone will remain intact or not. Clearly, this crisis demonstrates the huge strain the eurozone in under. That is why it was right for us to stay out of the eurozone."
Meanwhile, he admitted that there were many scenarios, which were being considered.
He said it "will not be appropriate" to talk about the detail, but "I will be guilty of not stepping up to the responsibilities of his office if plans had not been made to cope with a default."
He said that the UK banks had given around £2.47 billion in exceptional loans to Greek nationals and institutions.
Prime Minister David Cameron also declared that UK would not participate in a bailout of Greece.
"We were not involved in the first bailout of Greece; we don't believe the European financial mechanism should be used in any way."
Conservative MP Anne Main claimed that Greece "should be allowed to depart peacefully from the eurozone."
Danny Alexander, the Chief Secretary to the Treasury, also admitted that UK would not play a part in contributing aid package for Greece.
"The package for Greece that is already in place is a eurozone package with the IMF. It's the eurozone that is taking forward discussions now about the next stage of dealing with Greece's substantial problems. There's simply no proposition on the table for the UK to contribute beyond that IMF involvement and I don't expect there to be one," he said.
putting all your eggs in one basket - the euro didnt do anyone any favours except those that designed it to create an impossible political spiel -. one europe, one currency, one government and under it all, the communists.