Senior Whitehall sources said the Foreign Secretary will announce on Monday that the Bill paving the way for Britain's vote is to be put on hold.
The move, which follows 'no' votes by the French and Dutch, is a further sign the controversial treaty is in its death throes. Mr Straw is expected to tell MPs the Referendum Bill is to be put on ice indefinitely.
Europe Minister Douglas Alexander said public opinion could not be ignored. His words left no doubt that Tony Blair wants the constitution to be abandoned when EU leaders meet to discuss the crisis on 16 June. But German chancellor Gerhard Schroder and France's Jacques Chirac are refusing to accept the verdict.