Churchill opens his speech to Parliament by explaining what's happened over the past couple days:

On Friday evening last I received His Majesty's commission to form a new Administration. It as the evident wish and will of Parliament and the nation that this should be conceived on the broadest possible basis and that it should include all parties, both those who supported the late Government and also the parties of the Opposition. I have completed the most important part of this task. A War Cabinet has been formed of five Members, representing, with the Opposition Liberals, the unity of the nation. (2-5)

There are several important pieces of information here:

(1) The day Churchill was asked to be prime minister, replacing Neville Chamberlain, he put together his main cabinet of five members. Yes, the same day. The man wasn't wasting any time—there was a war on, after all.

(2) The cabinet he assembled to govern through the war is made up of men from different parties.

That shows that he's serious about creating a government that truly represents the people of the nation at this crucial time, when they'll have to make decisions that could impact the country in ways far beyond whether or not to raise taxes. Churchill's demonstrating that he's not in this for political power or gain, but to lead the entire country and be inclusive about it.

The opening lines aren't the riveting poetry that comes later in the speech, but they'd grab the attention of Parliament and calm everyone down. It's not like the MPs didn't know that Churchill had been made prime minister, but there was so much going on at the time, so who knows how well-informed they were about the state of the administration.