What's the best exercise if you're short of space?!

That depends on what you are trying to do. If it is to build endurance, what you suggested works. To build muscle, try isometric exercise. Back a few million years, when I was young, comic books carried ads for a course of exercise from Charles Atlas, which he called "Dynamic Tension", essentially pitting one muscle group against the other, as by putting your palms together and pushing. You could also push against an immovable object.

Pushups, jumping jacks, burpies, crunches, squats, etc. Those are some basic low-space exercises.

Jumping jacks, run in place, and crunches.