Can I work from home while sick?

I'd make a distinction here: it depends how sick you actually are. Being bedridden with a cold is different from having a mild runny nose while working from home - if you're really wiped out to the point where you need to sleep, your boss should leave you alone, but checking a few emails isn't automatically illegal as long as it doesn't strain you.

A sick note doesn't mean you're absolutely forbidden from doing anything, it means you're not fit for your regular job - dashing off a quick email is a totally different thing from bringing full work capacity.

Legally speaking, here's how it works: a medical certificate confirms that you're unable to work, and that includes not putting strain on yourself through work and risking your recovery. Your boss can't simply force you to answer emails.

What's often overlooked: even if you feel well enough to reply to a few messages, that can cause problems for your doctor later if your cold drags on - they might then view the medical certificate critically. In short, tell your boss politely that you've gotten a medical certificate and therefore shouldn't be doing any work tasks.

The problem isn't really even the legal side - it's about your recovery. When you're signed off sick and lying in bed, your body is telling you it needs rest. Processing emails, even if it's "just a few," pulls you in mentally and prevents you from properly recovering. In the end, you'll just need longer to get back on your feet. Your boss should understand that a sick note isn't a part-time solution - either you're working or you're unfit to work.