The eggs look like Green Shield Bug eggs - harmless, so not an issue,, though its probably wise to keep any eye on them to see what hatches out.
If possible, a picture of the plant itself would be useful, but note that older leaves on Fatsia do yellow and then go black and fall off, sometimes even younger ones if they're in the middle of the bush and very shaded. The other cause of yellowing and blackening, usually at the top parts, is sudden frost after a warm spell, or excessive wind.

I agree

Thank you Bamboo and Noseypotter. Shield bugs would make sense. The only similar (identical, in fact) eggs I could find on the web were those of brown marmorated stink bugs, which are a big problem in the US and many parts of Europe but, as far as I can establish, they don't occur in the UK. I've isolated the eggs anyway to see what hatches. They'll probably turn out to be shield bugs but, if they are stink bugs, do I need to record and report it?

I've hacked the plant back considerably as it had grown so thick and bushy it was cutting out the light (it is virtually directly outside my window) so all there is to photograph at the moment is the stumps with some healthy growth and a huge heap of amputated limbs... which is how I encountered the eggs.

it will soon come back ront as for the bugs . why not you have nothing too lose .

These eggs are just plain green, reminiscent of birds eye peas in fact... stink bug eggs do vary in colour, but the green ones have what look like smiley faces on them - black and brown marks. They have been found in Ukraine in June 2012, but no reports of their being here yet. If you want to check now, pick one or two off and crush them - if they're stink bugs, they'll stink....

Thank you all for your input. The eggs have now hatched and I'm trying to figure out how to post photos on this thread. Failing that, I go back to my profile and upload from there.