It's very rare for a laptop to need the ground even though they always make it a possibility. I'm pretty sure you are fine.

If there IS an issue (due to improper design of the laptop), you should feel a slight buzz when touching certain surfaces on the laptop while it's been turned on for a while. If you don't, I can't imagine you need to worry about it.
Pokun wrote:
For the refrigerator I can't because there is no earth cable from what I can see.
Isn't there a screw terminal on the back of it? (probably with
this icon) You could just find som isolated copper wire and screw it on there. That's what I did with my New Astro City cabinet, which is coincidentally Japanese hardware, so I imagine it's the standard there. If there isn't one, then it's not needed for the refridgerator.
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For the washing machine I'll probably need a new cable shoe as it's just a loose fringe harness of copper threads. Unless you can just screw it in under the screw thingy that covers the earth outlet or something.
You can just do that, and you're probably expected to do it like that. I would make sure the power is off before doing it though

In fact, you might even want to discharge it into the ground plug before touching the uninsulated part, just to be sure! I wouldn't be surprised if this kind of thing builds up a lot of static.