In this situation it sounds like the risk is of the floor above collapsing. If the inspector considered this a risk to adjoining properties (unlikely) they could be compelled to have the work done, or a council appointed contractor would eventually do the work and they would be billed.
Most...
Get the spare beds ready. If it's dangerous they'll be out the house the day it gets inspected.
Edit: May be able to put in a couple of acro props and stay in house until remedied. If Brighton area feel free to pm me nearer time, won't take long to collect some and put them up.