Drilling metal is not a hard problem, but it requires a little more finesse. When you get your tools, feeds and speeds dialed in just right, it cuts like a dream. But do it ham-handed, and you can work-harden the steel. No fun!
They make combo bits for wood and steel meant for power drilling. A drill bit intended for wood will not work. A drill bit will tend to be rough to control; it won't cut clean or neat. Normally you punch holes in metal with a drill press or punch, e.g. a floor mounted Rotex or turret punch.
Doing it with hand tools is a challenge. Your best bet is a punch, especially since you've already got a hole there. Here's one punch for instance. Drill a pilot hole, assemble it, tighten the bolt, and it cuts the hole. This particular one is for ~20mm holes, but they make them in many sizes.
If you can get a power drill, I would use a step drill bit to expand an existing hole.