That speech does tend to make me well up almost every time I hear it. Its continuation is highly revealing too:
"... We shall never surrender, and if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old. "
It's not just an appeal to the British to never give up, but an appeal to the United States to join the War and turn the tide.