Many thanks to each of you.
I think the Sale of Goods Act issues have been very well covered by the immensely helpful folk over at Money Saving Expert and another helpful chap working for Trading Standards at the Citizens' Advice Bureau. I now know what to do, and have sent off a letter to the Managing Director of Bathstore. I'm hoping that will get us somewhere, but the missus is asking me how I propose to sort out her bathroom if Bathstore refuse.
I have heard that some products like this are made in the Far East and sold under a variety of different names. The Euro Trio style is quite distinctive, so I was hoping someone might have seen them under another name at a different seller. That's the real point of my enquiry here.
To pick up the other good points made:
chapeau: Someone at MoneySavingExpert also suggested getting the credit card company involved. I will look into that - thanks!
securespark: I am as sure as anyone could reasonably be that the item was delivered broken. Bathstore's carrier placed it in my front room along with all the other stuff I ordered, and I did not touch it. The plumber carried it a few feet whilst I was in the next room before opening the box to fit it. He has been very careful doing all this work. I didn't hear him drop it or anything like that, but as soon as he opened one end, he saw it was damaged and called me.
Bathstore's "no quibble replacement policy" only applies if you tell them within 7 days. At least that's what the three different Bathstore people I spoke to all said rather emphatically. We didn't find the problem until day 13 or 14. It strikes me that 7 days to notify delivery problems is a bit of a swizz as they also say to allow 7 days between expected delivery and start date for installation.
big-all: Good points, thank you. Chasing up the Sale of Goods angle already. The Distance Selling Regulations aren't relevant in this case. Even though I ordered over the internet, more than 7 days have passed, and I am not wanting to cancel the transaction, I want a replacement. (By the way, I think it's 7 days to notify under DSRs, not 14 to return - I've been learning more than I ever wanted to know about consumer rights in the last few days!)
Thanks again, all. Please do let me know if you come across a white bathroom cabinet made of marine ply with curved corners.