I don't think any cultural service can consider itself immune from cuts and they are a bit of a soft option being nice to have rather than being essential. I love the Horniman but I love essential services more and would prefer to sacrifice the former to the latter. I don't think we have seen anything yet re the cuts in public facilities and services.
I do hope that the Horniman won't be proceeding with its rather expensive expansion plans in the current climate? That would hardly be prudent.
I was thinking today of some of the museums I visited in the past in Eastern Europe where the curators opened up each room for guided tours one at a time and turned the lights on and off and in any case were only open one or two days a week to save money. It may sound like a joke but I suspect that this might turn out to be reality in these times of austerity. Some of us remember the time when TV went off at 10pm in order to save power so perhaps its not that far fetched.