The issue was briefly raised at the first meeting of Labour's joint Shadow Cabinet and national executive commission on the constitution after Mr Straw, a member of the commission, said it was of 'the first importance' that Labour should 'think through its own response to the current crisis' affecting the monarchy.
Tony Blair, Labour's home affairs spokesman, was said to be relaxed about Mr Straw's intervention in a speech in Blackburn this week.
The Labour environment spokesman said that while affection for the Queen was undiminished, support for the institution of monarchy was 'palpably declining.' The choice was between 'moving towards a much tighter and more limited constitutional monarchy on the Dutch or Scandinavian models, or embracing the idea of a republic', he said.
Issues such as the Queen's powers to call and recall Parliament are set now to be debated in the commission - powers that would anyway be diluted by Labour's backing for fixed-term parliaments.
Some MPs saw Labour heading into dangerous territory. Graham Allen, Mr Blair's deputy as spokesman on constitutional matters, said Labour had a full agenda on constitutional reform, but 'that does not and will not include the future of the monarchy or its powers'.
However, Mo Mowlam, the Shadow Cabinet member responsible for the Citizen's Charter, was reported yesterday to support a close examination of the royal prerogative, while another Shadow Cabinet member welcomed Mr Straw's intervention, declaring 'it should all be looked at'.