You could try putting down a mulch such as bark chips Robert. It doesn't grow very tall and would be smothered. The mulch would help improve the soil over time, too.
I agree with Philippa, Sarcococca would be a much better bet and actually requires shade or part shade. Evergreen too.
You could be (and probably are) right nut. All of my 'collection' of buttercups have wider and less segmented leaves but given how prolific they are, it could just be a variant that doesn't grow around here.
If you look closely, I don't think it's a buttercup nut. The leaves look like some kind of poppy and are very similar to californian poppy, but I don't think it's that as it's an annual and wouldn't be that big at this time.
It does look very weedy though so I'd have it out too!
The strawberries look like they are being munched by slugs. Straw won't protect them against slugs, it is used to prevent the fruit from touching the ground which causes the berries to rot. Sprinkle a few slug pellets under the straw so the birds can't get to them or, if you don't want to use pellets, water Nemaslug into the area:
Doesn't take 5 minutes to spray them with glyphosate.
Red veined sorrel (aka Bloody sorrel)?
Edit: Oops - I think nut has it right - red veined dock!
Also known as Bloody dock (but I call all dock plants that!)
Edit 2: Same thing and apparently you can eat it but not sure I would:
I do grow honeyberry aym and can confirm they are happy in ordinary soil. You need 2 plants to pollinate and my crops are quite small so far after 3 years. They are early to flower (mine in flower now) so hoping there are enough bees about to do the business!
I need to write 'sow lettuce' on my arm I reckon as I keep forgetting and have none sown so far!
Jostaberries taste much like blackcurrants aym. They're a bit bigger though as is the bush so if only room for one I would recommend a blackcurrant.
Good idea fidget - the techie elves could perhaps hyperlink the title text of any Talkback threads back to the original article?