Straw said "no!"...
... so he had to go.
The new British Foreign Secretary is Margaret Beckett, the first woman to ever hold the position. She was also briefly leader of the (then opposition) Labour Party in 1994, holding the position as a 'caretaker leader' between the death of John Smith and the election of Tony Blair as leader. Originally from the hard left of the party, she is nowadays considered to be a loyalist in the Blair 'inner circle'. She first held ministerial office back in 1976 and since Blair's election in 1997, she has served as President of the Board of Trade, Leader of the House of Commons, and Secretary of State for Environment, Food and Rural Affairs. Interestingly, she expressed reservations in the run up to the Iraq War, but supported the 2003 Iraq War when the time came.
So perhaps, some subtle - or not so subtle - indications are now coming from London...
Most mysterious of all is how the office of 'prime minister' evolved (for example no-one can tell you for sure when the office originated.
