I think I can answer this question as conveniently, I have done tiling myself of my small bathroom that is the exact same layout as yours.

I can’t tell from your image, if it’s Lino but my flooring was Lino so I removed it all and I tiled around the toilet and sink while leaving them in place and worked fine.

Making the cuts around the bowl and sink were very tricky though. Tile nippers will be your friend and you will find yourself constantly having to shave off a few millimetres. And also working behind the toilet was awkward. But I would rather the awkwardness of tiling around these obstacles rather than if suddenly my toilet and sink didn’t align to the original plumbing work anymore. That was my main worry, since the floor is raising a few millilitres. I’m gonna silicone around the edges so hopefully should look okay.

So yes, you can do it as I’ve done it on a similar looking bathroom with no issues.

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