Thanks for advice so far!

Yes Toom, by level I meant horizontal.

The wonkiness is the sum of both a gradual trend from one side of the
room to the other and more localised peaks and troughs (over distances
of about 2 or 3ft in a 10ft by 10ft room).

Colin you are right, the more localised variation was already quite
obvious. I think it was the extent of the difference from one side of
the room to the other that most surprised us. Which perhaps would
suggest that the advice of following the overall trend but not the
local variations would work best.

Dave's point about how old coving would have moved had there been some
there the same age as the ceiling is a good one.

Cheers,

Clare.