Hm! Why would anyone *want* to expose any of that lot?

oh, I could see why - the OP just wants to expose the purlins, not
necessarily the whole roof space. Would give additional height to the
bedroom as well. Presumably the exposed rafter ends would be covered and
made good with plasterboard.

Exactly.

What puzzles me is why the joists have sagged - is this likely to be just
the weight of the ceiling pulling down on them? I thought that ceiling
joists would normally be in tension - keeping the rafters from spreading and
maintaining the integrety of the walls. The purlins should presumably
supported at each end by the walls, but there couldn't be any chance that
these joists are, for some reason, taking the weight of these purlins,
causing them to sag?

No. The joists aren't touching the purlins. Some of the joists
actually have "scoops" cut out of them in order to stop them from
touching the purlins.

In any case, this is non-trivial stuff potentially affecting the structural
stablility of the house, and if I was the OP then I'd want to get the (paid)
advice of a structural engineer

Happy to do that

Armed with this info I don't see any reason why a competent DIYer following
proper practise for the work couldn't tackle the job...

It looks so straightforward - cutting bits of wood and nailing them in
(I know it's a bit more involved than that in reality).

Thanks,

John