You're not fat, I'm the same weight as you (as far as I'm aware) and an inch shorter but you carry the weight better than I do (as in, it looks nicer)
But I know from my own bmi I am slightly overweight, but not fat.
Just exercise and have a reduced calorie diet to start off with, the NHS have a good plan thing that you can monitor it. I think it's been suggested to lose only like 1-2lb a week, especially if you don't want the flabby skin after (not sure if this is right, just something I've seen a bit)