Aside from people (obviously?)
Tablet, phone (and charging stuff), purse, keys, maybe grab passport if possible but it wouldn't be a pressing urge to do so.
Everything else can be replaced.
tablet and phone - mainly because they contain precious photos and phone also bloody useful in enabling me to find shelter etc for dd and I.
Purse - bank card so can access cash/pay for accommodation/food and other essentials, also for ID purposes.
Keys for if it will be possible to re-enter home at a later point to retrieve more stuff.
Passport - if I remember. Mainly because pita and expensive to replace!
In the past I had certain items of jewellery I'd probably have tried to rescue but sadly these have been lost anyway 
I've been in house fires, evacuated due to a gas leak and homeless very unexpectedly twice so I think about this sort of thing a lot.
Those experiences also taught me that "stuff" really doesn't matter. The vast majority can be replaced over time and you really don't miss it.
I have also lost things like photos of loved ones who had since passed and that kinda thing you DO miss. So much easier with being able to "save" such things electronically now.
"Oh and essential medicines" ah! Good call, yea I'd grab our meds too as they're murder to get hold of (one of mine a "controlled" one so particularly difficult to arrange replacement on say a bank hol weekend)
"it infuriates me to see news stories of folk who have lost things in floods and fires etc who aren't insured." Not everyone can afford insurance, but yes I agree those who really can definitely should.
Were you working in the field when there was the flooding in 2007? Iirc there were quite a few families who'd been unable to get or get decent insurance due to their homes being on known flood plains (WHY was/is that allowed?)
"Remember folks that toiletries even medicines would be supplied in such circumstances" I'm not sure working on that assumption is a good idea though. Eg not all pharmacies carry my meds, plus there'd still be a limited supply to go around so those who can grab their own should I think, so that pharmacists and Drs could then reserve their help for those who were unable to do so.