You need to figure out exactly how they put it together and work back.

Did you write Haynes manuals in a former life?
Lol

"Reassembly is the reverse ..." etc...

Anyway, looking as closely as I can at the fixing, it still looks like some kind of star washer arrangement rather than a security screw, so it seems to me that the only likely ways to get the cover off are to drill the fixing out or break the washer off somehow - both options pretty unappealing. I thing I'll just have to splash out £30 for a new toaster. Many thanks to everyone for the suggestions and comments - I managed to find our old toaster in the loft today (a Braun model, c. 1995) so at least have something usable (it doesn't do thick bread or crumpets, though, which is why we got a new one), and note that the bottom panel is metal and fixed using screws.. Clearly there are some ways in which technology has gone backwards...