Can I prune a fatsia japonica plant?

You can prune them, yes. Now is a good time. Cut just above a branch/leaf junction to the shape you want. Surprisingly, you can be brutal with these too and chop them right back and they'll still survive (although personally, I wouldn't do that).

These can grow huge, in fact, I'm wondering how much bigger mine's gonna get, although i'm loathe to prune it or touch it 'cause I love it just as it is at the mo.

one that i had had an accidental strimming when hubby used his new toy. I was convinced it was a goner but no it came back bigger than ever. so dont worry.

Thank you Llew and Seaburngirl. I think I will be brave and prune some branches hard this year and follow up with more of the same next year. Hopefully it will be easy from then on.

yes you can, not a problem