The first one looks like a Croton, but it's not. I forget the name of it. I think it begins with an A. The second one appears to be English Ivy.

I would lean towards a variety of croton b/c leaves are too big to be Aucuba. Plant is sickly, perhaps excessive moisture Or insufficient light. Second one reminds me of a variety of Hedera helix

Oh no, why do you think the croton is sickly? It came like that!

The first could well be Aucuba japonica..,.....leaves on this shrub can be as much as 8" long. Although the lack of any teeth or serrations on the leaves would indicate the croton more likely.

The second is Fatshedera lizei, a cross between Fatsia japonica and English ivy

Thank you floral_UK! I'm glad to hear it's not sickly. I didn't suspect it to be a croton as we have one already and its leaves are wavy rather than straight like this one.

Any good tips on either croton or English ivy/fatsia japonica care would be most welcome! :)

Maybe stressed is a better word than sick. But going by their size, I’d guess they were grown in a hothouse and some plants react adversely to the change as I’m betting your house is cooler. It doesn’t mean they can’t take cold, just that they respond quickly to sudden change. ALA you don’t overwater and keep in sunniest spot possible, it should recover. Yellowing leaves in this plant w/b a red flag to me and cue to keep a close eye for a bit.

T-R-O-U-B-L-E

That's my identification of the plants in question. Lol

Now that I'm more awake. The first is a Croton that needs a lot more light. It's trade name was "Sloppy Painter" but it's actual name, from the book, is Eleanor Roosevelt. You can just make out the shoulders on two of the leaves. I grew this one for years in South Florida. It's an old timer in the Croton world.

Maybe Croton 'Gold dust'? I just saw many in local GH, with that ID...