It is normal, but if you think about it, it doesn't really take an hour to eat lunch - and sometimes it would be preferable to eat in 5 minutes and leave at 4:05 instead of taking an hour to sit around the office. Every reasonable employer would permit this but I have learned from reading HN comments that not every employer is reasonable.
Break times also tend to be regulated in most countries I believe. I.e. here in Japan 60 minutes break time is required if you work for more than I think about 6ish hours.
When I used to work in Japan I hated that rule. One day I feeling not so great, so I took the morning off. But we had an important release, so I still went to the office in the afternoon. The release ran into few issues, so I had to stay past the regular finish time of 6pm. I started to feel no so great again, so I wanted to finish the release and head home as soon as possible. But at 7pm, my boss came running towards me and forced me to take one hour break. I tried to explained to them (unsuccessfully) I only have about 5-10mins to finish the release. So I spent another one hour with watering eyes, massive headache, and chills, just to finish 5mins of work.
I mean, it's a sensible regulation but there should be some leeway for edge case situations like yours (if there aren't already - since you were actually sick that should make it OK for you to leave ASAP one would hope)
