Julia can you post this on Doghouse and The Litter Tray too.
I'd imagine dogs and cats would be the most requested pets needing help in these dreadful situations.
Charities like The Cinnamon Trust who help walk dogs when their owners are in hospital or unable to get out for whatever reason.They advertise for volunteers too but I bet there are not nearly enough.
Are Dogs Trust looking for people to take the animals into their homes (rather than going round to the house to take the dog out)
Very 
, Something many people probably haven't even thought about. And one reason why so many animals gets abandoned, dumped or ignored.