It was previously showing on screen but now I can't find it, even when the object with the subdivision surface modifier is selected. I have managed to apply a modifier via searching the modifier but I'm unable to modify its properties .
You have accidentally pinned the Properties Editor when you had a different item selected. So now, even though you clearly have a mesh selected, you don't see the Modifiers, as the properties editor shows you information about something else.
Click the PIN needle to unpin the editor, then everything should be back to normal: