Yes, I'm sure it's the offset. Having spent all morning looking at other pics on cars with the same arches as mine, and also with similar-looking 5" rims, I was confused as to how the others looked fine, but mine didn't.
It seems that standard "Minilikes" have an offset of around 31, whereas those described sometimes as "deep dish" have an offset of around 14. I've just measured my car and that 17mm will make all the difference. Unfortunately, Minispares makes no mention of the offset on the product page for the wheels I bought, so it seems it's a case of caveat emptor.
Because I've fitted the wheels (although they haven't moved an inch), Minispares considers them second-hand and isn't interested in helping me, so not much to do but shop elsewhere and try to sell on the Minispares wheels in due course. It'll be an expensive lesson, but there you go 