Complex sentence: Milne reported the contact and position but neglected to tell the Admiralty that the German ships were heading east and so Churchill still expected them to threaten the French transports--he authorized Milne to engage the German ships if they attacked the transports.
Split into simpler sentences: Milne reported the contact and position, but neglected to inform the Admiralty that the German ships were heading east. Churchill therefore still expected them to threaten the French transports, and he authorized Milne to engage the German ships if they attacked the transports.