It was not a stock expression. After Churchill used it in that speech, that particular phrase became associated with that speech and with Churchill. The phrase "This was their finest hour" is a Churchill _quotation_.
Another one is "Never was so much owed by so many to so few."
And another is "We shall not flag or fail. We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender."