Even without Leach’s intervention, she would have sent out the task force. Why? Her own instincts were strongly in favor; she would have been ashamed to acquiesce in the surrender of British territory to fascist aggression–and that’s how it was seen in Britain at the time.
But even if she had quailed before an admittedly formidable task, parliamentary and public opinion would have pushed her into it. You had to hear the special parliamentary debate to believe it. Almost the whole House (with a handful of exceptions like Tony Benn, the George Galloway of his day) was passionately in favor of military action.
Michael Foot, reliving his youth as an anti-fascist partisan, was no less firm than Enoch Powell predicting grimly that the next few months would show “of what metal she [the Iron Lady] is made.” At that stage, she would not have survived as prime minister if she had gone for a fudged diplomatic solution. Which suited her fine.