Yup another one here who refers to going into London as going to town, whereas the City is a square mile where most of the financial sector is based.
And tbh honest it's a great area. Steeped in history, wonderful architecture, great restaurants, bars and shops. Good vibe.
Though actually some banks, law firms etc moved out to get bigger gaffs but still refer to themselves as City.
I guess it's become a word that denotes a type of work.