Hi there
I don't remember it myself but I DO have an old ordnance survey map from the 50s. When you say Eldon Square do you mean the green bit with the war memorial, if so all the lanes surrounding it were called Eldon Lane....bit boring really! But I think the Cafe Royal is/was on Nelson St on the other side of the road....so I've attached a bit of the map (I hope, first time I've tried it!) that might help jog your memory
mo