That pic is Commander Christopher Louis Wreford - Brown DSO Royal Navy. HMS Conqueror after sinking the Belgrano. His father was one of my lecturers at BRNC Dartmouth. I served in the South Atlantic and Persian Gulf and it was insisted upon that we called it The Jack or Union Flag.
Quite right. The flag in question is the Union Flag.
The flagstaff at the bow of a warship is called the Jackstaff, and the flag which is flown on it is therefore referred to as the Jack. This is not unique to the Royal Navy, it's also true on ships of the US Navy for example, who also call the flag flown there the Jack.