Community leaders are urging David Cameron to reverse the government's decision to end support for the rescue of refugees trying to reach Europe.
The Foreign Office has said it would not back future search-and-rescue operations to prevent migrants drowning in the Mediterranean.
A petition set up by the Jewish Council for Racial Equality (JCore) has received over 370 signatures asking the Prime Minister to reverse the decision.
The letter refers to the Jewish refugee experience and calls on the government to join other European states in continuing to support rescue efforts.
JCore said the government's move had been a shock. It said: "This is not an issue of immigration or economics, but of ethics and morality. The announcement has revealed that Britain's respect for the sanctity of human life has all but vanished.
"Many in the Jewish community come from families who themselves had to escape persecution and find safety as refugees in the UK and elsewhere."
Rabbi Natan Levy, Board of Deputies social action consultant, signed the petition. He described the government's decision as "indefensible".
He said: "As a Jew, my DNA is encoded with the plight of refugees since the leaving of Egypt. I shudder to imagine if Great Britain had turned away the Kindertransports with the same easy indifference as they are now letting families die in the sea.
"This is a serious injustice and we cannot be silent."
Foreign Office minister Baroness Anelay said rescue operations could encourage more people to attempt to make the dangerous sea crossing to enter Europe.
Around 150,000 migrants, from North Africa and the Middle East, have been rescued by Italian ships over the past 12 months.
Some 3,000 migrants have drowned this year.