See, this is what puzzled me. The bolt in the brake caliper doesn't go all the way through the fork. It goes into the fork and there is a nut or something literally inside the fork which it is screwing into.
It rather makes me wonder how the brake was fitted in the first place, given what you've said above, as the only way I could get the brake off in the first place was to remove the wheel and detach the brake cable and then literally spin the entire brake caliper around to unscrew it from the captive nut inside the fork. That's the point at which I realised I wasn't going to be able to get the mudguard on as there would be no way I could get the guard in place and then spin the brake caliper back on.
Unless I use an allen key in the hidden nut to turn that? Though obviously I can't see in there to have figured that out myself!
I've found
a page at Sheldon Brown's site which has pictures of how a recessed nut is set up. I guess that might help me out a bit. At least then I could get the brake back on properly, and then worry about why it's not opening up properly. And I could get the mudguards on myself and would only be left worrying about why the brake doesn't work, which I can probably get a mate to help with.
Ah, and I've finally managed to find Tektro's own installation guide. That ought to help.