If you spend your lunch hours doing something active / outdoors - do you ever than have issues with people complaining when you are eating at your desk during your working hours?
I'm another one who worked in an environment where you didn't have time to take the lunch break you were entitled to (sorry but it's not unusual) - so that meant that most of us ate at our desks while working. If you're in an environment where people do take lunch breaks then I think people might object. It seems wrong for some people to use their lunch break to eat their lunch, and others to use their lunch break to do something else and then spend working time eating their lunch.
Back in the day when I did take a lunch break more often, I'd run errands as i worked in a small town eg bank or post office, drop off/collect dry cleaning or shoes heeling. I had my hair cut a couple of times, met friends for a quick lunch.
I did try having a swim once as a male colleague did this regularly and said it invigorated him for the afternoon. I'd overlooked the fact that his hair was dry by the time he was dressed and I needed time to dry mine and reapply a little makeup so that didn't work for me.